Question 836487
The two questions are quite different, even though they use the exact same words.


Suppose Lincoln Middle School has 100 students, so that 63 play an instrument, 45 play a sport, and 30 play both. We want P(sport|instrument), or the probability that a selected student plays a sport, given that he plays an instrument. There are 63 students who play an instrument, and out of those 63, 30 play a sport. The desired probability is 30/63 = 10/21.


The probability that a student plays an instrument given he/she plays a sport can be found similarly. 45 students play a sport, and 30 of these also play an instrument. The probability that a student plays an instrument, given that he plays a sport, is 30/45 = 2/3.