Question

In a class of students, the following data table summarizes how many students play an instrument or a sport. What is the probability that a student who plays an instrument does not play a sport ?

Answer 1

The probability that a student who plays an instrument does not play a sport is 4/15

Here, we want to calculate the fact that given that a student plays an instrument, what is the probability that the student does not play a sport

Let the event that a student plays an instrument be B and the event that a student does not play a sport be A

Thus, we have it that;

`\begin{gathered} P(A|B)\text{ = }(P(AnB))/(P(B)) \\ \\ P(AnB)\text{ = }(4)/(30) \\ \\ P(B)\text{ = }(15)/(30) \\ \\ P(A|B)\text{ = }(4)/(30)*(30)/(15)\text{ = }(4)/(15) \end{gathered}`