If a customer at a particular grocery store uses coupons, there is a 50% probability that the customer will pay with a debit card. Thirty percent of customers use coupons and 35% of customers pay with debit cards. Given that a customer pays with a debit card, the probability that the same customer uses coupons is .

The probability that a customer uses coupons given that the same customer pays with a debit card is P(C I D) = 0.428571 or about 0.43 (approximately 43%).

Step-by-step explanation:

This is a question regarding the concept of conditional probability. The general formula for this is:

(1)

We can read the former as the probability of the event A given the event B is the probability that these two events occur simultaneously divided by the probability of event B.

We have to identify the events in the problem. We call the events as follows:

Then, we have the next probabilities extracted from the question:

"If a customer at a particular grocery store uses coupons, there is a 50% probability that the customer will pay with a debit card" or

P(D|C) = 0.50

"Thirty percent of customers use coupons"

P(C) = 0.30

"...and 35% of customers pay with debit cards."

P(D) = 0.35

Then, the question is asking about P(C|D) = ?

Solving the question

Using formula (1) we can say that

Thus

But

Then

Solving the equation for P(C|D)

We already know the values for the right side of the equation and we can finally determine what the probability is. So

Thus, "given that a customer pays with a debit card, the probability that the same customer uses coupons is" 0.428571  (or about 0.43).

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