Question

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?

Answer 1

$p =q = 0.5$

$n = 5$

Using the binomial distribution,

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

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

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