A bag contains 15 marbles 6 black and 9 white Two marbles ar

A bag contains 15 marbles, 6 black and 9 white. Two marbles are drawn without replacement, which means that the first one is not put back before the second one is drawn. (round answers to three decimal places.)

(a) What is the probability that both marbles are black?

(b) What is the probability that exactly one marble is black?

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

a)
P( X = 2 ) = ( 2 2 ) * ( 0.4^2) * ( 1 - 0.4 )^0
= 0.16
b)
P( X = 1 ) = ( 2 1 ) * ( 0.4^1) * ( 1 - 0.4 )^1
= 0.48