A baseball player has a batting average of 0.2. What is the probability that he has exactly 3 hits in his next 7 at bats?

Question

The probability is

Answer 1

Binomial

p=0.2 ; q = 1-p = 1 - 0.2 = 0.8;

N=7; k=3; N-k = 7-3=4;

Prob(X=3)

(N choose k)(p)^k (q)^(N-k)

(7 choose 3) (0.2)^3 (0.8)^4

(7*6*5*4 / 3*2) (0.2)^3 ( 0.8)^4 =

(7*5*4) (0.008) ( 0.4096) =

0.45875

= 45 and 7/8 %