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

Answer:

$\frac{9}{35}$

Step-by-step 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 $\frac{9}{21}$

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 $\frac{12}{20}$

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

$\frac{9}{21} * \frac{12}{20} = \frac{9}{35}$