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 kept the money, given that the student was given four quarters.

Accepted Answer

Welcome back, everyone. A cafe analyzed whether customers tips 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 did not tip, given that the customer paid by card? A 0.50, B 0.60, C 0.70, and D 0.05. For this problem, we are dealing with a conditional probability because it says given, right? That's our keyword. We can define the probability as the probability of no to. Given that the customer paid by card. Because we're given a table, we don't need to use the formula for our conditional probability. What we have to do is, first we'll narrow down and identify the customers who paid by card. So we're given a AO which says paid by card, right? And now we want to identify the customers who left no tip in the same row. And essentially we can see that 18 left a tip and 42 did not tip. So essentially we're going to label these numbers. No tip is 42 within the category of those who paid by card. And now what we have to do is identify. The number of customers who paid by card, that would be 18 + 42, right? We have to find the total, that's 18 + 42. Now what is the probability? Well, it is the ratio between two numbers. The number of favorable outcomes in the numerator. So we're looking for those who did not tip, and that's 42 in the numerator, and our denominator is the total number of customers, right? The total number of outcomes. We are going to add those who left a tip and those who did not tip, which results in the total number of customers who paid by card because that's our category. So we're adding 18 + 42 in the denominator, and that's it. We have to perform the calculation, which is 42 divided by 60. When we divide these numbers, we get 0.70, which corresponds to the answer choice C. Thank you for watching.

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Key Concepts

Probability

Conditional Probability

Data Interpretation

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