SOLUTION: At Lincoln Middle School 63% of the students play a musical instrument, 45% play a sport, and 30% play a musical instrument and a sport. What is the probability that a student Linc

Question 836487: At Lincoln Middle School 63% of the students play a musical instrument, 45% play a sport, and 30% play a musical instrument and a sport. What is the probability that a student Lincoln plays a sport, given that the student plays an instrument? What is the probability that a student at Lincoln plays an instrument, given that the student plays a sport?
My goal is to try and solve this problem several different ways, with graphs, algebraically, and using system of equations if possible. I am having trouble approaching this problem because to me the last two questions seem to ask the same thing. Can someone explain this problem more clearly and then help me set up a probability.
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
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.
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