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SPE-MATH2 WEEK1-17 - NOTES
Bachelor in Secondary Education (BSED 4101- S)
Bestlink College of the Philippines
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WEEK1: Number and Number Sense
Addition as the combining together of the elements of two sets. This step by step way of obtaining an answer is called an algorithm. We also have, algorithms for subtraction, multiplication and division. Each of these operations is called a binary operation because only two numbers at a time can be operated on or combined together. To add 12 + 15 +10, we have (12 + 15) + 10 = 27 + 10 = 37, or 12 + ( 15 +10 )= 12 + ( 15 + 10 ) = 12 + 25 = 37. This property of addition is called the associative property. In general, if a, b and c are three numbers, then ( a + b ) + c = a + ( b + c ) The commutative property of addition. In general, if a + b represented two numbers, then a + b = b + a In subtraction; Joe started with 85 garlands of sampaguita. After an hour, he had sold 48 of them. How many more had he to sell? •What are we asked for? The remaining number of garlands Joe had to sell.
- What is given? He had 85 garlands at the beginning.
- What operation do we have to use? Subtraction. In solving the problem there are two methods; a. Expanded form minuend -----> 85 = 80 + 5 = 70 + 15 subtrahend --> - 48 = = 40 + 8 = 30 + 7 difference --------------> = 37
b. Short method 7 15 8 5 4 8 3 7 In both addition and subtraction, we have given the expanded form algorithm to help you understand the procedure. However, to solve problems, always use the short method.
Multiplication and Division Multiplication as a short- cut for repeated addition. example: Mic buys 4 tickets to a play and each costs Php 20, How much he has to pay? Thus, four tickets cost 20 pesos + 20 pesos + 20 pesos + 20 pesos. You can just simply get the answer by 4 × Php 20 Properties of Multiplication If you let a, b, and c represent any numbers, a. Commutative property. When factors interchange does not affect the products. 15 × 10 = 10 × 15 b. Associative property. Groupings of factors interchange does not affect the products. 6 × ( 9 × 4 ) = ( 6 × 9 ) × 4
c. Distributive property over addition. Multiplying a sum by a number gives the same result as multiplying each addend first by the multiplier and then adding the products. a( b + c ) = a × b + a × c or a( b + c) = ab + ac
WEEK2: Ratio and Proportion
- Ratio is an ordered comparison of quantities of the same kind. It can be expressed as a fraction.
- When each term of a ratio is multiplied or divided by of the same none zero number, the ratio remains the same. •A proportion is a statement of equality between two ratios. It can be written in the form a/b = a:b = c:d
- In the proportion a : b = c : d, the outer numbers a and d are called extremes and the inner numbers b and c are called means. The product of the extremes equals the product of the means. In symbols, a/b = c/ d, ad = bc,
- When two ratios are equal, they form a proportion.
- To solve a missing term in a proportion, use the cross-product method.
- If two quantities are so related to each other that an increase (or decrease) in first causes an increase (or decrease) in the second , then this is called direct proportion. If two quantities are so related to each other that an increase ( or decrease) in the first quantity causes a decrease ( or increase ) in the second quantity, this is called inverse proportion.
WEEK3: Percent
Finding percent of a number involves multiplication Multiplying percent To multiply a number by any percant, convert the percent to its equivalent decimal number,then multiply. To multiply by 1% move the decimal point of the multiplicand two places to the left to obtain the answer. To multiply by a fraction of 1%, first get one percent of the number and then multiply this product by the fraction part of the percent given. Example: 1/3 % of 300 means 1/3 of 1% of 300 1/3 of ( 1% of 300 ) = 1/3 × 3 = 1 The aliquot parts of 100% are called the fractional equivalents. These aliquot parts are used to shorten computatoon.
Aliquot Parts = Fractional Aliquot Parts = Fractional Aliqupt Parts = Fractional Equivalent Equivalent Equivalent
10% = 1/10 90% = 9/10 66 2/3% = 2/ 20 % = 1/5 25% = 1/4 16 2/3% = 1/ 30 % = 3/10 75 % = 3/4 83 1/3% = 5/
The set of integers include positive and negative numbers and zero. Integers can be represented on a number line. On a number line, the set of integers are arranged this way. Greater --------> Smaller <-------- <---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|--> -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6 +7 +8 +9 + Negative Numbers (- ) Positive Numbers ( + )
WEEK7: BASIC OPERATION OF INTEGERS
Addition of Integers Rules:
- To add two or more integers with the same sign, add the absolute values of the addends. The sum has the same sign as the addends. ex. +47 + + 32 = +
- 47 + - 32 = -79+37 + (+ 21) + ( +10) + (+5) = +
- 37 + ( -21) + ( -10) + (-5) = -
- To add integers with unlike signs, find the difference of their absolute values. The sum Will have the sign of the greater obsolute value. ex. Add: 4 + (-9) step 1. | - 9 | - | 4| = 9 - 4 = 5 step 2. 4 + ( - 9 ) = -
- Suntraction of Integers
- To subtract an integer, add it opposite.
- The difference has the sign of the number with the greater absolute value. Example 1 : Subtract + 12 - + 6 Step 1. + 12 - + 6 = + 12 + ( - 6 ) ( The opposite of 6 is - 6. ) Step 2. + 12 - + 6 = + Example 2 : Subtract + 13 - + Step 1. +13 - + 19 = + 13 + ( - 19 ) ( The opposite of 19 is - 19 ) Step 2. + 13 - + 19 = - 6 Example 3 : Subtact + 6 - ( - 4 ) Step 1. +6 - ( - 4 ) = +6 + +4 ( The opposite of -4 is 4. ) Step 2. + 6 - ( - 4 ) = + 10 Example 4: Subtract : - 11 - ( - 2 )
Step 1. - 11 - ( -2 ) = - 11 - ( - 2 ) ( The opposite of - 2 is 2 ) Step 2. - 11 - ( - 2 ) = - 9
- Addition and Subtraction of Three or More Integers Three ormore integers can be added or subtracted by the successive application of the rules. Example 5: + 7 + ( -4 ) - (-1) Solution: Step 1. Add the first two numbers.
- 7 + ( - 4 ) = + 7 - +4 = + Step 2. Add the result of step 1 to the third number.
- 7 + (-4 ) - ( - 1 ) = + 3 - ( - 1 ) = +3 + +1 = + Example 6 : Find 9 - 6 + 5 + 2 - 3 - 7 - 8 - 9. Solution: Step 1. Group the positive and negative numbers separately.
- 9 + +5 + +2 = 16
- 6 + - 3 + -7 + -8 + - 9 = - 33 Step 2. Add the results of step 1.
- 16 + - 33 = - 17
- Multiplication of integers Rule 1. When both integers are positive, then tbe product is also positve. example 1: +6 × +7 = +7 + +7 + +7 + +7 + +7 + +7 = +42 or + 7 × +6 = +6 + +6 + +6 + +6 + +6 + +6 + +6 = + Rule 2. When the integers are of unlike sign, theirproduct is negative. example 2: +5 × -6 = -6 + -6 + -6 + -6 + -6 = 30 Therefore: +5 × -6 = - Rule 3. When both integers are negative, then their product is positive. example 3: -5 × -3 = + Rule 4. The product of any integer and 0 is 0. example 4: +9 × 0 = 0-9 × 0 = 0
- Division of Integers Study the following:
- If the dividend and the divisor have like sign, then the quotient is positive. example: a. 21 ÷ 7 = 3 b. -270 ÷ -9 = 30
- If the dividend and the divisor have unlike signs, then the quotient is negative. example: a. 150 ÷ 30 = - b. - 200 ÷ 5 = - What happens if the dividend or divisor is zero? Study the following:
-2 × -2 = +4 +2 × +2 = +
-3 × -3 = +9 +3 × +3 = +
-4 × -4 = +16 +4 × +4 = +
-5 × -5 = +25 +5 × +5 = +
-6 × -6 = +36 +6 × +6 = +
-7 × -7 = +49 +7 × +7 = +
-8 × -8 = +64 +8 × +8 = +
-9 × -9 = +81 +9 × +9 = +
-10 × -10 = +100 +10 × +10 = +
From the given list of multiplication, we see that +100 is the square of +10 as well as -10. Hence, both +10 and - are square roots of 100. Similarly, +8 and -8 are the square roots of +64; +6 and -6 are the square roots of +36, and so on. We use the symbol " √ " to denote the square root of a number. Thus ±√144 = ±12. Not yet done!
Week 9: Geometry and Measurement
There are lots of objects around us that can be identified as polyhedrons. A visit to a grocery store exposes us to many spatial figures or three-dimensional objects that have simple closed surfaces. A solid figure with flat surface is a polyhedron. The flat surfaces are called faces. The faces intersect to form edges. The edges intersect to form vertices. A prism is a polyhedron with two parallel equal bases that are shaped like polygons. The other faces of a prism are shaped like parallelograms. A prism is named by the shape of its bases. Some three-dimensional figures have curve surfaces. A cone has a circular base and one vertex. A cylinder has two parallel equal circular bases. A sphere is a solid with all points the ssme distance from a given point called the center. For prism and pyramids, the surface area is the sum of the area of the polygonal faces. Example 1: Find the surface area of a rectangular box with side lengths 3 cm and 5 cm and height 2 cm. Solutoon: W e can disassemble the box into 6 rectangles Each area of the base is 3 x 5 = 15 square centimeters. For the lateral surface, the area is 2[( 3 x 2 ) + (5 x 2 )] = 2(6 + 10 ) = 2( 16 ) = 32 sq cm
The total surface area is 2(15) + 32 = 30 + 32 = 62 sq cm. Example 2: Find the surface area of a cylinder with diameter 8 cm and height 12 cm.
Solution: Take a cylinder can of milk with paper label. Remove the label without destroying it. Spread open. To find the surface area of the cylinder, add the area of the two circles and the rectangular surface area.
Area of top and bottom circles = 2( pie r square) = 2( 3 × 4 square) = 2 ( 3 × 16 ) = 2 ( 50) = 100. 48 sq cm
Area of rectangular surface = 2 pie rh = pie d x 12 = ( 3. 14) (18)(12) = 301 sq cm The surface of the cylinder is 100 + 301 = 401 cm square. Pyramids The surface area of a pyramid is obtained by adding the areas of the triangular faces amd the base. Example 3: Find the surface area of a right square pyramid whose base measures 16 cm on aech side and whose faces are isosceles triangles with edge of length 10 cm. Solution: The total surface area equals the area of the base plus the areas of the lateral faced. The base is a square with side 16 cm. Its area is ( 16) square= 256 cm square. The lateral faces triangles. Before we can find the area, we must first find the altitude h. Each face is an isosceles triangle h square + 8 square = 10 square h square = 100 64 h square = 36 h = 6 cm The area of each face is one half (16) (6) = 48 sq cm. The surface area of the square pyramid is 4( 48 ) + 16 square = 192 + 256 = 448 sq cm
So the total surface area of a square pyramid is Area of the square base + 4 × Area of the triangular face. If the base of the pyramid is an equilateral triangle, then the total surface area of the triangular pyramid becomes Area of the triangular base +3 × Area of the triangular face. Thus, for any pyramid with regular polygons as a base, we determine the total surface area by the following formula: Area of the base + 4 × Area of tje surface Cone A cone is also a solid figure. Its base is not a polygon. A right circular cone has a circle for its base.
So, the surface area of the sphere is 7234 cm square.
WEEK10: Volume of Solids
The volume of prisms, cubes, and cylinders can be calculated bymultiplying the area of the base by the height. V = B × h Where B = area of the base h = height of the prism Example 1: The edge of a cubical box measures 7cm. What is the volume of the box? V = B × h = ( 7cm × 7cm ) × 7 cm = 343cubic cm Example 2: A cylindrical can with radius 3 cm and height 7 cm is used to transfer water from a big jar to a pitcher. How much water can the cylindrical hold? Solution: Calculate the volume of a cylinder. The base of a cylinder is a circle. V = B × h = pie r square × h = 22/7 × ( 3 cm ) square × 7 cm = 22/7 × 9 sq × 7 cm V = 198 cubic cm
Volume of Prisms and Pyramids A prism has two bases while a pyramid has only one base. It' s pretty obvious that having the same base and height a pyramid will have less volume than a prism. How much less? When they have the same measurements of base and height, It needs three times the content of the pyramid to fill the content to Example 3 : A rectangular prism has a base length of 4 cm, a base width of 3 cm, and a height of 5cm. Compare the volume of this prism to a pyramid with the same measurements. Solution: Find the volume of the prism and the volume of the pyramid. V ( prism ) = B × h B = 4 cm × 3 cm = 12sq h = 5 cm V = ( 12 sq. cm ) × 5 cm V = 60 sq. cm
V (pyramid )= 1/3 × B × h B = 4 cm × 3 cm = 12 sq. cm h = 5 cm V = 1/3 × 12 sq × 5 cm V = 1/3 × 60 cu = 20 cu The volume of a pyramid, 20cu, is one third the volume of a prism, is 60cu.
Volume of Cylinders and Cones
Just like prisms and pyramids, the volume of a cone is only 1/3 of the volume of a cylinder with the same dimensions. It tales 3 cones to fill a pyramid.
Example 4: A metal cone with a radius of 7 meters and a height of 4 meters is used to fill a cylindrical glass of the same dimensions with oil. How many of the cone's capacity Will fill the cylinder full?
Solution : Compute the volume of the cylinder and the volume of the cone. V ( cylinder ) = B × h B = pie r square = 22/7 × ( 7 cm ) square = 22/7 × 49sq = 154 sq h = 4cm V = 154 sq × 4 cm V = 616 cu
V ( cone ) = B × h B = pie r square = 22/7 × ( 7 cm )square = 22/7 × 49 sq = 154 sq. cm h = 4cm V = 1/3 ( 154 sq ) × 4 cm V = 205 1/3 cu V = 616 cu ÷ 205 1/3 cm = 3 Answer: 3 times Volume of Cylinders and Sphere
V ( sphere ) = 4/3 pie r cube V ( cylinder )= pie r h A cylinder will fit exactly around the sphere if they have the same radius. In that case, the height of the cylinder is the diameter of the sphere and the volume of the sphere will be 2/3 of tge cylinder's volume.
Example 5: A globe and a cylindrical shaped jar each have a radius of 21 cm. Compare their volume if the jar fits exactly around the globe. Solution: Use the formula to calculate the volume of a sphere and the volume of a cylinder. V ( sphere ) = 4/3 pie r cube r = 21 cm V ( globe ) = 4/ 3 × 22/7 × (21 cm ) cube = 88/21 × 9 261 cu. cm = 38 808 cu V ( cylinder = pie r square x h r = 21 cm , h = 2 × r = 42 cm V ( jar ) = 22/ 7 × ( 21cm )square × 42 cm = 22/7 × 441 sq × 42 cm = 58 212 cu
To find the number of cubic meters of water consumed, subtract the previous reading from the present reading. Present reading: 1339, Previous reading: 1318, Consumed: 20 cu m and 559 liters or 20 cubic m
Examples: Look at these water meter rebisters 0000,070 This is read as 70 L or 0 cubic m ( 70 liters or 70 thousandths cubic meter) 0000,567 This is read as 567 L or 0 cubic meter. ( 567 liters or 567 thousandths cubic meter) 0075, 987 This is read as 75 cubic meter ( This is read as 75 cunic meters + 987 liters.)
WEEK13: Data Collection
Statistics is defined as the science that deals with the collection, presentation, analysis, and interpretation of data. Data is a collection of facts, such as numbers, words, measurements, observations or even just descriptions of things. Descriptive information are qualitative data while numerical information are quantitative data. Example 1. The following information are gathered about the Grade 6 class. Identify which data are quantitative and which are qualitative. a. The class is noisy. b. There are 24 boys and 26 girls in the class. c. The class loves to watch basketball games. d. The class average in math is 92. Answers: a and c are qualitative data. These statements are descriptions of the class. On the other hand, b and c are quantitative data. They provide numbers in the information. Methods of Collecting Data A statistical process starts with collection of data. Consider this scenario. A teacher would like to find out whether the use of calculators would improve the performance of her grade 6 students in mathematics. Before she can make her conclusion, she must first gather information and analyze those. Data can be collected by any of the following methods:
- Use of questionnaire A questionnaire is a set of questions prepared by the one who is conducting the study. The answer to the questions become his basis in the conclusion that he will make. A questionnaire may be mailed to the respondent. It may also beadministered directly to the respondent.
- Interviews
Another method of gathering information is by conducting interviews. Although questions to be asked are also prepared before hand, these questions are more open ended. The interviewer can ask follow up questions right away based from the answers of the respondent. 3. Experiments Data can also be gathered by performing experiments. However, the experiment must be designed such that the necessary data required by the study will be obtained. 4. Observation
Observing the respondents' behavior, attitudes and reactions also provides valuable information to one who is conducting the study. Population and Sample Suppose the math club officers want to determine the most and the least liked subject of the students in their school. They prepare questionnaires for the students to answer. The respondents are the students of the school.
- All the students of the school is called population. If the officers decide to make every student of the school to become respondents of their study, then they are conducting a census.
- The officers may opt to collect data from selected students only. The selected respondents are part of the population and is called sample. Example 2. Which would be more practical to use in each of the following cases - sample or population? a. The causes of car accidents in Commonwealth Avenue in Quezon City. b. The number of people using a certain brand of soap in a city. c. The number of voters who will vote for a specific candidate as president of the country. Answers: a. Population. In this case, an accurate analysis of all accidents would be required. b. Sample. It would be very expensive and time-consuming to ask every person in the city the brand of soap that they are using. c. Sample. It would be impractical to ask every voter of the entire country who they are going to elect as president. When deciding on the sample to be used, there must be no prejudice or bias. The sample must reflect the characteristics of the whole population. A sample that is unfairly influenced by the collection process is called a biased sample. Example 3. What could be a possible bias if a telephone survey is conducted to a sample during office hours? Answer: The sample would be biased towards people who stay at home during office hours. Those people who go to work will not be included in the survey. Sometimes, people used biased samples to promote their products or ideas. Do you think this is a good practice.
WEEK14: Pie Graph
Lesson Proper
Data gathered can be presented in many ways. The previous lesson presented data in graphical form. In this lesson, data will be presented in table form or tabular form, specifically, stem-and-leaf plot and frequency table.
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Repeat the same procedure for all the numbers in the set of the data. After completing the tally, fill up the frequency column and determine the total. Ages Tally Frequency 8 I 4 9 I I I I – I I 7 10 I I I I – I 6 11 I I I I – I I I 8 12 I I I I 5 30 Just like the stem-and-leaf plot, we can also interpret the data easily if they are organized in a frequency table. For example, we can see that only 5 members are 12 years old but there are 8 members who are 11 years old.
WEEK15: Tabular Presentation of Data, Range , Mean , Median , and
Mode
Topic: Statistic and Probability Sub Topic: Tabular Presentation of Data, Range , Mean , Median , and Mode
IV. LESSON PROPER
Data gathered can be presented in many ways. The previous lesson presented data in graphical form. In this lesson, data will be presented in table form or tabular form, specifically, stem-and-leaf plot and frequency table.
Stem-and-Leaf Plot
Stem-and-Leaf Plot, also called stem-and-leaf diagram, quickly summarizes numerical data. This is done by placing the data in a table such that some digits are regarded as stem while some are regarded as leaves. The examples below illustrates how this is done.
Example 1. Construct stem-and-leaf diagram for the following scores in mathematics obtained by the students: 75, 67, 78, 79, 87, 67, 88, 91, 95, 55, 77, 76, 75, 87, 91, 92, 83, 83, 85, 88, 80, 76, 67, 50, 98, 63.
Solution: Construct a two-column table. Column 1 will contain the stem and Column 2 will contain the leaves. Since the data are all two-digits, use the tens digit as stem and the ones digits as leaves. Generally, the last digits of the given numbers are placed on the leaves column.
By inspection, the tens digit are 5, 6, 7, 8, and 9. We place the numbers in the stem column, one in each row. Then we write the corresponding ones digits in the leaves column. For example, for the score 75, we locate the row where 7 is, and place 5 in the leaves column.
Stem Leaves
5 5, 0
6 7, 7, 7, 3
7 5, 8, 9, 7, 6, 5, 6
8 7, 3, 8, 7, 3, 5, 8, 0
9 1, 5, 1, 2, 8
What we have done above is an unordered stem-and-leaf plot. We can arrange the leaves in increasing order to have an ordered stem-and-leaf plot.
Stem Leaves
5 5, 0
6 3, 7, 7, 7
7 5, 5, 6, 6, 7, 8, 9
8 0, 3, 3, 5, 7, 7, 8, 8
9 1, 1, 2, 5, 8
From the ordered stem-and-leaf plot, we can easily see that the lowest score is 50 and the highest score is 98. We can also see that 8 students got scores between 80 and 88 inclusive and only 2 students got a score below 60.
Frequency Table
Another method of presenting the data is to use a tally-and-frequency table.
WEEK16: Making Simple Predictions and Possible Outcomes
If you roll a die repeatedly, then how many times do you think will a 4 come up? Or any one of the other five other numbers? Lest us find out through this activity. Perform the following experiment with your partner to see what actually happens. Roll a die six time while your partner records the results. Then, let your partner roll the die six times while your record the data. Complete the table by finding the frequency of each of the numbers coming out in the 12 rolls.
- An experiment is any procedure that can be done repeatedly and has a well-defined set of possible outcomes.
- Outcomes are the results of an experiment.
- A sample is a small portion of the large group.
- A trial is performance or repetition of an experiment. In the game of Tic–Tac–Toe, a player can win, lose, or draw. Players take turns placing X and O to try to get three in a row up, down, or diagonally. If the correct strategies are followed: The player who moves first will not lose. The player who moves second will not lose. What should happen if two people play 20 games of Tic–Tac–Toe? You know that many questions come up when we play games. Is skill more important than luck? Does every player have an equal chance to win? What is likely to happen on the next turn? Now you will see how to use math to figure out your chances of winning or losing. Fold a 3 by 5 index card along its width, but a little off center. If you toss the card up, then how will it land? Will it ever land on edge? How many times would each of the four possible outcomes happen in 100 tosses? Use a table like the one below to record your guesses. Large side down Small side down On edge Tent shaped Your guess out of 100 Actual count
- Toss or drop the folded card 100 times. Make sure it falls at least a few feet. Keep a record of each landing. Then complete your table.
- Which outcome occurred most often? Did you guess this result?
- In what position will your card probably land if you toss it one more time?
- Toss the card. Were you right? Do you think the most probable event is the one that will definitely happen?
- How can collecting data help you predict the outcome of future events? Consider the numbers 1, 3, and 4. Suppose we want to determine the total two–digit numbers that can be formed if these numbers are combined. Let us assume that no digit is to be repeated. The possible two–digit numbers that can be formed are: 13 14 31 34 41 43 There are 6 possible outcomes.
When a coin is tossed once, there are two possible outcomes: head or tail. Each outcome is equally likely. This means head and tail have equal chances. Let us consider the last digits of the mobile numbers: Ignore the other digits. What are these possible digits? The possible last digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Therefore, there are 10 possible outcomes. Outcomes are possible results in an experiment. How do we determine all the possible outcomes of an experiment? The Tree Diagram A tree diagram is like natural tree which starts from a single trunk and spreads out into branches, twigs, and leaves. It is a device to enumerate all the possible outcomes of experiments.
- Outcomes are possible results in an experiment
- A tree diagram is a device to determine all the possible outcomes.
- Multiplication Rule for Counting If one thing occurs in A different ways and another occurs in B different ways, then the two can occur together A × B ways.
WEEK17: Probability
Is there a chance that it will rain today? Chances of an event happening is called a probability of that event. If there is absolutely no chance that it will rain today, we say the probability is zero. However, if we are very sure, 100%, that it will rain today, we say the probability of raining is 1. The probability of an event is a number describing the chance that the event will occur, with this number ranging from 0 to 1. Events that are most likely to happen have a probability greater than 1/2 or 0. Those that are unlikely to happen have probabilities close to zero. There are two types of probability: theoretical and experimental. How do we differentiate the two? When we are asked this questions: “What is the probability of getting a head when you toss a coin?” Since there are only two possible outcomes, head and tail, you might say the probability of getting a head is 1/2 or 0. This is theoretical probability. This is what you expect to happen. In this case, if you toss a coin 10 times, you would expect that head will turn up 5 times and tail 5 times. But this may not always be the case. When you actually toss a coin, you may not get the head 5 times. Therefore, the probability of getting a head may not be 1/2. This is called experimental probability. This is what actually happens when you perform the experiment. Example 1: Consider the days of the week. If you choose a day at random, the probability that it is a Monday is 1 out of 7, or 1/7. The probability that the day you choose begins with the letter T is 2 out of 7, or 2/7. The probability that the day you choose has less than 15 letters Is 7 out of 7, or 1. The probability of an impossible event, such as choosing a day with only 3 letters, is 0 out of 7, or 0. Example 2: Perform this activity. Pick a Color Materials: A box, 6 marbles (3 green, 2 blue, 1 red) Groups: 5 students Procedure:
- Put the marbles in the box. Without looking, draw one marble from the box and record the color in the table below. Color
SPE-MATH2 WEEK1-17 - NOTES
Course: Bachelor in Secondary Education (BSED 4101- S)
University: Bestlink College of the Philippines
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