finite help math

Question

A fair coin is flipped 4 times and the result of Heads or Tails is recorded following each flip. Find the conditional probability that both Heads and Tails occurred during the 4 flips given at least 1 flip was Heads.

Answer 1

B=event at least one head and P(B)=15/16

A=event both H and T occurred and P(A)=14/16=P(A∩B)

P(A|B)=P(A∩B)/P(B)=(14/16)/(15/16)=14/15