Question

A high school baseball player has a 0.307 batting average. (This means that the probability that he will get a hit in any given at-bat is 0.307.) 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 = 0.307

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)*(0.307^0)*(1-0.307)^(8-0) = 8!/[(8-0)!*0!]*(0.307^0)*(0.693^8) = 0.0532

and P(1 hit) = Combination(8,1)*(0.307^1)*(1-0.307)^(8-1) = 8!/[(8-1)!*1!]*(0.307^1)*(0.693^7) = 0.1885

So, we get

Probability of at least 2 hits = 1 - (0.0532+0.1885) = 1 - 0.2417 = 0.7583

So, the required probability of getting at least 2 hits is 0.7583