A retail store accepts either Master or American Express cre

A retail store accepts either Master or American Express credit card. 60% of its customers carry American Express, 40% carry American but not Master’s. Among the customers who have Master card, 30% also carry American Express. What percentage of its customers carry exactly one of the two credit card types that the store will accept?

Solution

Let

A = american express
M = mastercard

THe question is asking P(A only or M only).

Thus,

As

P(A) = 0.60

P(A only) = 0.40

Then

P(A n M) = 0.60 - 0.40 = 0.20

As

P(A|M) = 0.30

Then

P(M) = P(A n M) / P(A|M) = 0.20/0.30 = 0.666666667

Thus,

P(M only) = P(M) - P(A n M) = 0.66666667 - 0.20 = 0.4666666667

Thus,

P(A only or M only) = 0.40 + 0.4666667 = 0.86666667 [ANSWER]