Denomination Effect
In Exercises 13–16, use the data in ...

Question

Denomination Effect

In Exercises 13–16, use the data in the following table. In an experiment to study the effects of using four quarters versus a $1 bill, some college students were given four quarters and others were given a $1 bill, and they could either keep the money or spend it on gum. The results are summarized in the table (based on data from “The Denomination Effect,” by Priya Raghubir and Joydeep Srivastava, Journal of Consumer Research, Vol. 36).

Denomination Effect

a. Find the probability of randomly selecting a student who spent the money, given that the student was given four quarters.

Accepted Answer

Welcome back, everyone. A cafe analyzed whether customers tipped based on their payment method. Some customers paid with cash while others paid by card. The results are shown below. What is the probability that a customer left a tip given that the customer paid with cash? We're looking for the probability of P tipped. Meaning the probability of a customer leaving a tip, given that the customer paid with cash. For this problem, because we're given the table, we don't need to use a formula of conditional probability. What we can do is simply narrow the table down, right? It says that first of all we have to ensure that the customer paid with cash and we're given AO which says paid with cash. So what we're going to do is simply express our probability as a fraction. We have to recall that our denominator contains the total number of outcomes, and in this case that would be the total number of customers who paid with cash. So essentially we have to add 33 those who left a tip, that's 33 + 17, those who did not tip. So we got 50, right? So our denominator where the total number of outcomes is 50, and our numerator is going to be the number of outcomes that are favorable, right? So we're looking for customers who left a tip, and that's 33 based on the table. So our numerator is 33, and that's it. All that we have to do is divide 33 divided by 50. Gives us 0.66. So the probability is 0.66. Thank you for watching.

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Key Concepts

Probability

Conditional Probability

Data Interpretation

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