Question

The credit department of Lion’s Department Store in Anaheim, California, reported that 26% of their sales are cash, 27% are paid with a credit card, and 47% with a debit card. Twenty percent of the cash purchases, 86% of the credit card purchases, and 61% 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.)

A) Probability:

Answer 1

P(cash) = 0.26

P(credit card) = 0.27

P(debit card) = 0.47

P(more than $50 | cash) = 0.2

P(more than $50 | credit card) = 0.86

P(more than $50 | debit card) = 0.61

P(more than $50) = P(more than $50 | cash) * P(cash) + P(more than $50 | credit card) * P(credit card) + P(more than $50 | debit card) * P(debit card)

                            = 0.2 * 0.26 + 0.86 * 0.27 + 0.61 * 0.47

                            = 0.5709

P(cash | more than $50) = P(more than $50 | cash) * P(cash) / P(more than $50)

                                       = 0.2 * 0.26 / 0.5709

                                       = 0.091 (ans)