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 3 of those games are won by the Colonials? Round your response to at least three decimal places.

Answer 1

In above problem, P(win) = P(not win) = 1/2 = 0.5

This is a direct application of Binomial distribition.

Let X be a number of games won by the Colonials among 5 games.

Here, X ~ Binomial ( n = 5, p = 0.5)

probability mass function of X is,

P(X = x) = ⁿC_x p^x (1 - p)^n-x

We want to find, P(X = 3),

P(X = 3)

= ⁵C₃ * (0.5)³ *(1- 0.5)^5-3

= 10 * (0.5)³ * (0.5)²

= 10 * (0.5)⁵

= 10 * 0.03125

= 0.3125

=> P(X = 3) = 0.3125

Therefore, the probability that exactly 3 of those games are won by the Colonials is 0.3125