According to a health survey, the probability that a participant is a male is 0.51 whereas the probability that a participant is a female is 0.49. The probability of selecting a participant who smokes cigars, given that the participant is a male, is 0.09. However, the probability of selecting a participant who smokes cigars, given that the participant is a female, is 0.02. Calculate the following probabilities (see the Hints below for the definition of the symbols): a. Probability of selecting a participant who is a cigar smoker (i.e., P(C)) (4 Marks) b. Probability of selecting a male participant given that the participant smokes cigars (i.e., P(M|C)) (3 Marks) c. Probability of selecting a female participant given that the participant smokes cigars (i.e., P(F|C)) (3 Marks) [Hints: let M, F and C be Male, Female and Cigar smoker respectively. Then, P(C) = P(C n M) + P(C n F) = P(CIM)*P(M) + P(C|F) )*P(F)]