Using conditional probability:
\(P(M|CC) = \frac{P(M and CC)}{P(CC)}\)
To find probability that one is both male and uses credit card, you multiply the two probabilities:
\(P(M and CC) = 0.55 * 0.1 = 0.055\)
To find probability that any person uses a credit card, you add the male and female probabilities:
\(P(CC) = P(M and CC) + P(F and CC) \\ \\ P(CC) = 0.055 + (0.45)(0.02) \\ \\ P(CC) = 0.064\)
Sub these values into original conditional probability:
\(P(M|CC) = \frac{0.055}{0.064} = 0.859\)
