Question

The credit department of Lion's Department Store in Anaheim, California, reported that 30% of their sales are cash, 30% are paid with a credit card, and 40% with a debit card. Twenty percent of the cash purchases, 90% of the credit card purchases, and 60% 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?

Answer 1

Hence the probability that she paid cash is 0.105

Explanation:

P(cash) = 0.3

P(credit card ) = 0.3

P(debit card ) = 0.4

P ( more than $50 | cash ) = 0.2

P (more than $50 | credit card ) =0.9

P (more than $ 50 |debit card ) = 0.6

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 * 0.3 + 0.9 * 0.3 + 0.6* 0.4

= 0.57

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

= 0.2* 0.3 / 0.57

= 0.105