Question

12 yellow balls and 9 red balls are placed in an urn. Two balls are then drawn in succession without replacement. What is the probability that the first ball drawn is a red ball if the second ball drawn is yellow?

Answer 1

`(9)/(35)`

Explanation:

When the first draw is done there are 9 red balls in a sample size of 21. So there probability of drawing a red ball will be
`(9)/(21)`

When the second draw is done, there will be 12 yellow balls in a sample size of 20 since the first ball will not have been replaced into the bag. So the chance of someone drawing the second ball in the second draw is
`(12)/(20)`

The probability of them happening in this order is the product of both probabilities:

`(9)/(21)  * (12)/(20)  = (9)/(35)`