A high school baseball player has a 0.174 batting average. In one game, he gets 6 at bats. What is the probability he will get at least 2 hits in the game?

Answer 1

This is the binomial probability. We will use the following parameters: n = 6 , p = 0.174 where p is the success probability of hitting the baseball.

C(6,2) = 6! / (2!*4!) = 15

C(6,3) = 6! / (3!*3!) = 20

C(6,4) = 6! / (4!*2!) = 15

C(6,5) = 6! / (5!*1!) = 6

P(X ≥ 2 hits) = [15*(0.174)² × (0.826)⁴] + [20*(0.174)³× (0.826)³] + [15*(0.174)⁴× (0.826)²] + [6*(0.174)⁵× (0.826)] = 0.2114 + 0.05938 + 0.009381 + 0.0007905 = 0.2809515 ≈ 0.2810

The probability of a high school baseball player gets at least 2 hits in the game is about 0.281.