Question

A high school baseball player has a 0.326 batting average. In one game, he gets 5 at bats. What is the probability he will get at least 3 hits in the game?

Answer #1

Please note

Binomial Probability = ^{n}C_{x} *
(p)^{x} * (q)^{n-x}, where n = number of trials and
x is the number of successes.

Here n = 5, p = 0.326, q = 1 – p = 0.674 .

_____________________________________________

P(At least 3) = P(3) + P(4) + P(5)

P(X = 3) = ^{5}C_{3} * (0.326)^{3} *
(0.674)^{5-3} = 0.1574

P(X = 4) = ^{5}C_{4} * (0.326)^{4} *
(0.674)^{5-4} = 0.0381

P(X = 5) = ^{5}C_{5} * (0.326)^{5} *
(0.674)^{5-5} = 0.0037

Therefore P(At least 3) = 0.1574 + 0.0381 + 0.0037 =
**0.1992**

**__________________________________________________**

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