A batch of 467 containers for forzen orange juice contains 1

A batch of 467 containers for forzen orange juice contains 15 that are defective. Two are selected, at random, without replacement from the batch. Round your answers to four decimal places What is the probability that the second one selected is defective given that the first one was defective? What is the probability that both are defective?

Solution

a.
containers for frozen orange juice contains 15 that are defective.
probability that the second one selected is defective given that the first one was
defective = P( First is defective) * P(Second is also defective) = 15/467 * 14/466 = 0.000964

b.
P(both defective) follows a binomial
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( X = 2 ) = ( 2 2 ) * ( 0.0321^2) * ( 1 - 0.0321 )^0
= 0.00103