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Coin - Coin
Coin
Course
Software Engineering (CS391)
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Fayoum University
Academic year: 2021/2022
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####### El-Shorouk Academy
####### Higher Institute for Computer & Term : First
####### Information Technology
####### Year: 3rd
####### Department of Computer sciences
####### Instructor : Dr shaaban
Computer modeling & simulation
COIN PROBLEM
Use the one-digit Random Number (6, 3, 5, 0, 8) to
generate random observations for:
a) Throwing fair coin.
b) Throwing a biased coin, assuming that probability of
tail=30%.(unfair coin)
?? Implement c# programs to simulate these two problems ??
a)
Random numbers that are one-digit are from 0 -------> 9 [ten integer numbers].
Because the coin is fair, then the probability of head equal to the probability of tail =
50% , Means “P(Head)=50% & P(Tail)=50% “.
- Theoretical probability of Head ( H )= 50 %= 0.
- Theoretical probability of Tail ( T ) = 50 % = 0.
Means that , the random numbers that indicate to head are five numbers (50%) , say :
0,1,2,3,4 and the random numbers that indicate to tail are the other five numbers
which are: 5,6,7,8,9.
H -----> 0, 1, 2, 3, 4 0.
T -----> 5, 6, 7, 8, 9 0.
No. of .trails = 5 According to the number of random numbers that given in that
problem ( we have in that problem 5 random numbers then no of trails = 5 )
Then:-
(6, 3, 5, 0, 8 ) -------Random observations---------> (T, H, T, H, T )
Simulated probability of head = no. of repeating head / no. of trials.
Simulated probability of( head)=2/5=0.
Simulated probability of tail = no. of repeating tail / no. of trials.
Simulated probability of (tail)=3/5=0.
Error = Theoretical prob - Simulated prob * 100
Theoretical prob
Error of head = 0 – 2/5 * 100 = 20 %
0.
Unfair Coin
b)
Random numbers that are one-digit are from 0 -------> 9 [ten integer numbers].
Because the coin is unfair, then the probability of head isn’t equal to the probability
of tail , then from the given probability the probability of head = 70 % , because the
probability of tail = 30 % ( given ).
Then let the random numbers that indicate to head are seven numbers (70%) , say :
(0,1,2,3,4,5,6) and the random numbers that indicate to tail are the other three
numbers which are: (7,8,9).
- Theoretical probability of head = 70 % = 0.
- Theoretical probability of tail = 30 % = 0.
H -----> 0, 1, 2, 3 , 4 , 5 , 6 0.
T -----> 7, 8, 9 0.
Then:-
(6, 3, 5, 0, 8 ) -------Random observations---------> (H, H, H, H, T )
No .Of. trails = 5 ( because the number of random numbers is 5 numbers )
Simulated probability of head = no. of repeating head / no. of trials.
Simulated probability of( head)=4/5=0.
Simulated probability of tail = no. of repeating tail / no. of trials.
Simulated probability of (tail)=1/5=0.
Error= Theoretical prob - Simulated prob * 100
Theoretical prob
Error of head = 0 – 0 * 100 = 14 %
0.
####### Error of tail = 0 – 0 * 100 = 33 %
####### 0.
Conclusion:
- Error of head = 14 % which means that the probability of head increased by
####### 14 %, because the theoretical probability = 0 and then after compute simulated
####### probability it become = 0 then it increased ( 0 0 ) , means also the simulated
####### probability is greater than theoretical probability.
- Error of tail = 33 % which means that the probability of tail decreased by 33.
####### % , because the theoretical probability = 0 and then after compute simulated
####### probability it become = 0 then it decreased ( 0 0 ) , means also the simulated
####### probability is smaller than theoretical probability.
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Coin - Coin
Course: Software Engineering (CS391)
174 Documents
Students shared 174 documents in this course
University: Fayoum University
Was this document helpful?
El-Shorouk Academy
Higher Institute for Computer & Term : First
Information Technology
Year: 3rd
Department of Computer sciences
Instructor : Dr.farouk shaaban
Computer modeling & simulation
COIN PROBLEM
Use the one-digit Random Number (6, 3, 5, 0, 8) to
generate random observations for:
a) Throwing fair coin.
b) Throwing a biased coin, assuming that probability of
tail=30%.(unfair coin)
?? Implement c# programs to simulate these two problems
??
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