Question

The credit department of Lion’s Department Store in Anaheim, California, reported that 28% of their sales are cash, 24% are paid with a credit card, and 48% with a debit card. Twenty percent of the cash purchases, 86% of the credit card purchases, and 58% 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

Let the events

• C= Paid cash
• CC=Paid with a credit card
• DC=paid with a debit card
• >$50= purchase is for more than $50

We know the following probabilities

• 28% of their sales are cash: P(C)=0.28
• 24% are paid with a credit card: P(CC)=0.24
• 48% with a debit card: P(DC) = 0.48
• Twenty percent of the cash purchases are for more than $50: P(>$50|C) = 0.20
• 86% of the credit card purchases are for more than $50: P(>$50|CC) = 0.86
• 58% of the debit card purchases  are for more than $50: P(>$50|DC) = 0.58

The probability that Ms. Tina Stevens paid cash (event C) given that she made a purchase for more than $50 (event >$50)(Ms. Tina Stevens just purchased a new dress that cost $120) is

ans: The probability that Ms. Tina Stevens paid cash given that she made a purchase for more than $50 (Ms. Tina Stevens just purchased a new dress that cost $120) is 0.104