Question

# Ross and Rachel play chess. For any one game the probability of Rachel’s win is 0.35....

Ross and Rachel play chess. For any one game the probability of Rachel’s win is 0.35. If they are to play 8 times and the outcomes are independent of one another, what is the probability that Rachel will win exactly 4 games?

Solution'-

Let X: number of games win by Rachel

p= 0.35= probability of success

n=8 = Rachel play 8 time games whose outcomes are independent

Therefore, from above information

X~Binomial(n=8,p=0.35) distribution

Therefore, pmf of X is given by

Now here we have to find probability that, Rachel will win exactly 4 games.

That is,we have to find P(X=4) =?

Therefore,

Therefore,

Result:-

The probability that Rachel will win exactly 4 games is 0.1875

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