Question

A particular baseball team wins 68% of its games. Next week it will play 6 games. (a) What is the team’s expected number of wins during that week? (Round your answer to 2 decimal places.) (b) What is the probability that the team will win at least 5 games next week?

Answer 1

A particular baseball team wins 68% of its games.

The probability of winning the game is p = 0.68.

Next week it will play 6 games. n = 6

Let X be the number of games that the team wins.

X Binomial (n = 6, p = 0.68)

The probability mass function of X is

P(X = x) = nCx * px * (1 - p)n - x ; x = 0, 1, ....., n

              = 0                                ; otherwise

The pmf of X is

P(X = x) = 6Cx * 0.68x * 0.326 - x ; x = 0, 1, ...., 6.

              = 0                                  ; otherwise

a) Answer :

E(X) = n * p

        = 6 * 0.68

        = 4.08

The team's expected number of wins during that week is 4.08.

b) Answer :

P(X 5) = P(X = 5) + P(X = 6)

               = (6C5 * 0.685 * 0.321 ) + (6C6 * 0.686 * 0.320)

               = 0.3780

The probability that the team will win at least 5 games next week is 0.38.