Question

In a city, 55% of the adults are males. 10% of males use

credit card, whereas 2% of females use credit card. One
adult is randomly selected for a survey about usage of credit
card. Find the probability that the randomly selected person
is a male given that this selected person uses a credit card.

Answer 1

Using conditional probability:

`P(M|CC) = (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) = (0.055)/(0.064) = 0.859`