Question

Suppose that the New England Colonials baseball team is equally likely to win a game as not to win it. If 4 Colonials games are chosen at random, what is theprobability that exactly 2 of those games are won by the Colonials .

Round your response to at least three decimal places

Answer 1

Solution

Given that ,

Using binomial probability formula ,

P(X = x) = (_n C _x) * p^x * (1 - p)^{n - x}

P(X = 2) = (₄ C ₂) * 0.5² * (0.5)²

Probability = 0.375

Answer 2

here this is binomial distribution with paramter p=0.5 and n=4

hence probability of exactly 2 games won by Colonists = $\small \binom{4}{2}(0.5)^{2}(0.5)^{2}$ =0.375