Question

Joseph Czerniakow is the owner of a fish market. To better understand his business, Joseph asked his assistant, Rachel Hirsh, to record how customers make their payments. After several months of data collection, Rachel reported to Joseph that 30 percent of all fish market sales are cash, 30 percent are paid with a debit card, and the remaining sales are paid with a credit card. However, 20 percent of cash purchases, 90 percent of credit card purchases and 60 percent of debit card purchases are for sales over $100.

a) What percentage of fish market sales is $100 or less?

b) A customer just purchased a larger amount of fish that costs $130. What is probability the customer is going to pay by cash or debit card?

Answer 1

a)

P(over $100)=P(cash)*P(over $100|cash)+P(debit)*P(over $100|debit)+P(credit)*P(over $100|credit)
	=0.3*0.2+0.3*0.6+0.4*0.9=0.6

therefore t percentage of fish market sales is $100 or less =1-P(over 100) =1-0.6 =0.4 or 40%

b)

P(cash or debit card given over $100)

=(P(cash)*P(over $100|cash)+P(debit)*P(over $100|debit))/P(over $100)

=(0.3*0.2+0.3*0.6)/0.6 = 0.4 or 40%