Question

This problem is about a fast-food business. As it turns out, 60% of their business is via the drive-through window and 40% is counter-service. Data from the registers reveal that 70% of the transactions at the drive-through are via credit/debit cards, while 80% of the transactions at the counter are via credit/debit cards. (The other transactions are via cash.)

Find the following probabilities. Enter the answers in decimal notation rounded to three decimal places.

Hint: a tree-diagram or a contingency table can be very helpful.

a) What is the probability that a random transaction was via credit/debit card (CD) and was at the drive-through window (W)?

P(CD and W) =

b) What is the probability that a random transaction was via credit/debit card (CD) and was at the counter (IN)?

P(CD and IN) =

What is the probability that a random transaction uses credit/debit cards (CD)?

P(CD) =

What is the probability that a random transaction uses cash (CS)?

P(CS) =

(e) Knowing that a random transaction was via credit/debit card (CD), what is the probability that was at the drive-through window (W)?

P(W | CD) =

(f) If a random transaction was made at the counter (IN), what is the probability that cash was used (CS)?

P(CS | IN) =

Answer 1

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