in a class of students, the following data table summarizes how many students playing instrument or a sport. What is the probability that student plays an instrument given that they play a sport?

Question

play an instrument and a sport: 2

play an instrument but does not play a sport: 8

does not play an instrument but plays a sport: 10

does not play an instrument or a sport: 4

Answer 1

Inst. No Inst Total

Sport 2 10 12

No Sport 8 4

Since your only concern is "given that they play a sport", only the top row is involved (12 total). Of those, 2 play an instrument. P(I|S) = 2/12, or 1/6.