The probability that a high school student in in the marching band is 0.47
so,
The probability that a student plays a varsity sport is 0.32
so,
the probability that a student is in the marching band and plays a varsity sport is 0.24
so, we get
P(M∩V)=0.24
a student plays a varsity sport if we know she is in the marching band
so,
P(V|M)=(P(V∩M))/(P(M))
now, we can plug values
and we get
So,
the probability that a student plays a varsity sport if we know she is in the marching band is 0.51063......Answer