00:01
In this problem, we have been given a table which shows us how athletes are cross -classified according to gender and sport.
00:10
Now, we need to find the probability that a randomly chosen athlete is a runner if it is known that they are female.
00:16
So we need to find the probability of r given f if we consider r to be the event that an athlete is a runner and f to be the event that an athlete is a female.
00:27
So the probability that an athlete is a runner, given that they are a female.
00:33
So using the definition of conditional probability, this is equal to p of r intersection f divided by p of f.
00:41
Now consider p of r intersection f, that is the number of favorable outcomes divided by the total number of outcomes.
00:47
Now the total number of outcomes will be the total number of athletes considered here, and it is said that there are 200 athletes considered here.
00:55
So the total number of outcomes is 200.
00:57
Now since intersection represents and the number of favorable outcomes will be the number of athletes who are both runners and female.
01:05
And from the table, we can see that that number is 60...