Buster Posey of the San Francisco Giants had the highest bat

Buster Posey of the San Francisco Giants had the highest batting average in the 2012 Major League Baseball season. His average was .449. So assume the probability of getting a hit is .449 for each time he batted. In a particular game, assume he batted five times.

What is the probability of getting five hits in a particular game? (Round your answer to 3 decimal places.)

c.What is the probability of not getting any hits in a game? (Round your answer to 3 decimal places.)

Solution

Binomial Distribution

PMF of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
Where   
k = number of successes in trials
n = is the number of independent trials
p = probability of success on each trial

b)
P( X = 5 ) = ( 5 5 ) * ( 0.449^5) * ( 1 - 0.449 )^0
= 0.0182

c)
P( X = 0 ) = ( 5 0 ) * ( 0.449^0) * ( 1 - 0.449 )^5
= 0.051
d)

P( X < 1) = P(X=0) +   
= ( 5 0 ) * 0.449^0 * ( 1- 0.449 ) ^5   
= 0.0508
P( X > = 1 ) = 1 - P( X < 1) = 0.949