Question

A high school baseball player has a 0.215 batting average. In one game, he gets 8 at bats. What is the probability he will get at least 2 hits in the game?

Answer 1

we have p = 0.215

n = 8 and x is at least means x = any value greater 2 till 8

Using binomial probability, we get

Probability of getting at least 2 hits = 1 - [P(0 hit)+ P(1 hit)]

where P(0 hit) = Combination(8,0)*(0.215^0)*(1-0.215)^(8-0) = 8!/[(8-0)!*0!]*(0.215^0)*(0.785^8) = 0.144

and P(1 hit) = Combination(8,1)*(0.215^1)*(1-0.215)^(8-1) = 8!/[(8-1)!*1!]*(0.215^1)*(0.785^7) = 0.3159

So, we get

Probability of at least 2 hits = 1 - (0.1442+0.3159) = 1 - 0.4601 = 0.5398

So, the required probability of getting at least 2 hits is 0.5398?