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Question

The following table represents food purchase amounts and whether the customer used cash or a credit/debit card. One customer is chosen at random. Give your answer as a decimal out to at least 4 places.

	Less than $10	$10-$49	$50 or More	Total
Cash Purchase	18	20	9	47
Card Purchase	6	8	14	28
Total	24	28	23	75

a) Find the probability that the customer's purchasing method was a cash purchase or the customer spent $50 or more. 

b) Find the probability that the customer's purchasing method was cash purchase and the customer spent $50 or more. 

c) Find the probability that the customer's purchasing method was a cash purchase given they spent $50 or more. 

d) Find the probability that the customer spent less than $50. 

e) What percent of cash purchases were for $50 or More. Round percent to two decimal places. %

Answer 1

I have worked the solutions out to the problems in the attached video. Check it out and feel free to reach out if you have any additional questions. Take care!

Dr. C

Answer 2

(a) P(cash or ≥$50) = P(cash) + P(≥50) - P(cash and ≥$50) = 47/75 + 23/75 - 9/75 = 61/75 = 0.8133

(b) P(cash and ≥$50) = 9/75 = 0.12

(c) P(cash, given ≥$50) = 9/23 = 0.3913

(d) P(<$50) = (24 + 28)/75 = 52/75 = 0.6933

(e) P(≥$50, given cash) = 9/47 = 0.1915 = 19.15%