Answer to Question #191696 in Statistics and Probability for Isaak

Question #191696

Suppose that the New England Colonials baseball team is equally likely to win a game as not to win it. If 5 Colonials games are chosen at random, what is the probability that exactly 2 of those games are won by the Colonials?


1
Expert's answer
2021-05-11T14:47:52-0400

p=q=0.5p =q = 0.5

n=5n = 5

Using the binomial distribution,


P(X)=nCr(p)r(q)nrP(X) = ^nC_r(p)^r(q)^{n-r}


P(X=2)=5C2(0.5)2(0.5)3P(X=2) = ^5C_2(0.5)^2(0.5)^3


P(X=2)=5C2(0.5)5P(X=2) = ^5C_2(0.5)^5


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