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;
[tex]\begin{gathered} P(A|B)\text{ = }\frac{P(AnB)}{P(B)} \\ \\ P(AnB)\text{ = }\frac{4}{30} \\ \\ P(B)\text{ = }\frac{15}{30} \\ \\ P(A|B)\text{ = }\frac{4}{30}\times\frac{30}{15}\text{ = }\frac{4}{15} \end{gathered}[/tex]
