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.

Verified step by step guidance

1. Step 1: Understand the problem. We are tasked with finding the conditional probability of a student keeping the money, given that the student was given four quarters. Conditional probability is calculated using the formula P(A|B) = P(A ∩ B) / P(B), where A is the event 'kept the money' and B is the event 'given four quarters.'
2. Step 2: Identify the relevant data from the table. From the table, the number of students who were given four quarters and kept the money is 16. The total number of students who were given four quarters is 27 (purchased gum) + 16 (kept the money) = 43.
3. Step 3: Calculate the probability of event B (P(B)), which is the probability of a student being given four quarters. This is the total number of students given four quarters (43) divided by the total number of students in the study. To find the total number of students, sum all the values in the table: 27 + 16 + 12 + 34.
4. Step 4: Calculate the joint probability of events A and B (P(A ∩ B)), which is the probability of a student being given four quarters and keeping the money. This is the number of students who were given four quarters and kept the money (16) divided by the total number of students in the study.
5. Step 5: Use the formula for conditional probability P(A|B) = P(A ∩ B) / P(B) to find the final result. Substitute the values calculated in Steps 3 and 4 into the formula to determine the probability of a student keeping the money, given that they were given four quarters.

Key Concepts

Probability

Probability is a measure of the likelihood that a particular event will occur, expressed as a number between 0 and 1. In this context, it helps determine the chance of a student keeping the money given that they received four quarters. The formula for probability is the number of favorable outcomes divided by the total number of possible outcomes.

Conditional Probability

Conditional probability refers to the probability of an event occurring given that another event has already occurred. In this case, we are interested in the probability of a student keeping the money, conditioned on the fact that they were given four quarters. This concept is crucial for accurately interpreting the results of the experiment.

Data Interpretation

Data interpretation involves analyzing and making sense of data collected from experiments or surveys. In this scenario, understanding how many students kept the money versus those who purchased gum is essential for drawing conclusions about the denomination effect. Proper interpretation allows for insights into consumer behavior based on the type of currency given.