Musical styles other than rock and pop are becoming more popular. A survey of college students finds that 48% like country music, 30% like gospel music, and 10% like both. What is the conditional probability (±0.01) that a student likes gospel music, given that he or she likes country music

Answer 1

Conditional probability of A given B is given by
P(A|B)=P(A∩B)/P(B)
C=country, P(C)=0.48
G=gospel, P(G)=0.30
C∩G=both, P(C∩G)=0.10
P(gospel given country)
=P(G|C)
=P(G∩C)/P(C)
=0.10/0.48
=0.21

Answer 2

p(c)=0.48
p(g)=0.30
p(cng)=0.10

p(CuN)=0.48+0.30-0.10
=0.68