A batch of 350 samples of containers for frozen apple juice

A batch of 350 samples of containers for frozen apple juice contains 6 that are defective. Two are selected at random, without replacement from the batch. What is the probability that the second one selected is defective given that the first one was not defective? A batch of 30 samples of containers for frozen apple juice contains 5 that are defective. Two are selected at random, without replacement from the batch. What is the probability that both are defective?

Solution

1. there are 350 containers out of which 6 are defectives. 2 are chosen randomly without replacement.

now, probability that 2nd container is defective given that 1st container is not is

= p(1st container is not defective and 2nd container is defective) / p( 1st container is not defective)

now, p(1st container is not defective and 2nd container is defective) = (344c1*6c1)/(350c1*349c1)

p(1st container is not defective) = 344c1/350c1

so, the required probobaliy is

=(344 *6/350*349)/(344/350) = 0.017.

2. there are 30 containers out of which 5 are defectives. 2 are selected at random without replacement.

so, noumber of favourable cases = (5c1*4c1) = 5*4

number of total cases = 30c1*29c1 = 30*29

probability that both are defective = 5*4/30*29 = 0.023