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 = ⁿC_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 .

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

P(X = 3) = ⁵C₃ * (0.326)³ * (0.674)^5-3 = 0.1574

P(X = 4) = ⁵C₄ * (0.326)⁴ * (0.674)^5-4 = 0.0381

P(X = 5) = ⁵C₅ * (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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