Binomial Probablity

Question

A high school baseball player has a 0.256 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

Probability of 2 or more successes in 6 trials

That is the same as 1 minus Probability of zero successes minus 1 success

Prob(X>=2) =

1 - Prob(X<2) =

1 - [ Prob(x=0) + Prob(X=1) ] =

1 - Prob(X=0) - Prob(X=1)

p=0.256

k=0,1

N=6

Prob(X=0) =

(6 choose 0) * 0.256^0 * 0.744^6 =

1 * 1 * 0.744^6 = 0.169604594650054656

Prob(X=1) =

(6 choose 1) * 0.256^1 * 0.744^5 =

6 * 0.256 * 0.227963164852224 = 0.350151421213016064

THe probability is 0.48024398413692928 or just over 48%