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