Question

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?

Answer 1

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