An urn contains 12 balls 5 of which are red The selection of

An urn contains 12 balls, 5 of which are red. The selection of a red ball is desired and is therefore considered to be a success. If a person draws three balls from the urn, what is the probability of two successes?

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
P = Red = 5/12 = 0.4167

P( X = 2 ) = ( 3 2 ) * ( 0.4167^2) * ( 1 - 0.4167 )^1
= 0.304