Question

The credit department of Lion’s Department Store in Anaheim, California, reported that 24% of their sales are cash, 27% are paid with a credit card, and 49% with a debit card. Twenty percent of the cash purchases, 86% of the credit card purchases, and 51% 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

Dear Student, given question comes under the category of conditional probability. Here we have to find the probability of cash purchases when purchases are given to be more than $50.

Since I cannot paste tree diagram properly, I will try to to do it in typed only.

1. Cash Purchases Probab - 0.24 ----------------- a. 0.20 more than $50

------------------b. 0.80 less than $50

2. Credit Card Purchases Probab - 0.27 ----------------- a. 0.86 more than $50

------------------b. 0.14 less than $50

3. Debot Card Purchases Probab - 0.51 ----------------- a. 0.51 more than $50

------------------b. 0.49 less than $50

P(Cash Purchases given More than $50) = (Cash Purchases & More than $50) / [(Cash Purchases More than 50) + (Credit Purchases More than 50) + (Debit Card Purchases More than 50)]

= (0.24 x 0.20) / [(0.24 x 0.20) + (0.27 x 0.86) + (0.49 x 0.51)]  

= (0.048) / [(0.048) + (0.2322) + (0.2499)] = 0.048 / 0.5301 = 0.0905 or 9.05%