Question

The credit department of Lion’s Department Store in Anaheim, California, reported that 27% of their sales are cash, 26% are paid with a credit card, and 47% with a debit card. Twenty percent of the cash purchases, 81% of the credit card purchases, and 63% of the debit card purchases are for more than $50.

Ms. Tina Stevens just purchased a new dress that cost $120. What is the probability that she paid cash? (Round your answer to 3 decimal places.)

Answer 1

Bayes' Theorem: P(A | B) = P(A & B) / P(B)

P(she paid cash and purchase is more than $50) = 0.27x0.20

= 0.054

P(purchase is for more than $50) = P(she paid cash and purchase is more than $50) + P(she paid with a credit card and purchase is more than $50) + P(she paid with a debit card and purchase is more than $50)

= 0.27x0.20 + 0.26x0.81 + 0.47x0.63

= 0.5607

P(she paid cash | purchase is for more than $50) = P(she paid cash and purchase is more than $50) / P(purchase is for more than $50)

= 0.054/0.5607

= 0.096