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.

Verified step by step guidance

1. Step 1: Understand the problem. We are tasked with finding the probability of a student spending the money, given that the student was given four quarters. This is a conditional probability problem.
2. Step 2: Recall the formula for conditional probability: P(A|B) = P(A ∩ B) / P(B). Here, A is the event 'student spent the money' and B is the event 'student was given four quarters'.
3. Step 3: Identify the relevant data from the table. The number of students who were given four quarters and spent the money is 27. The total number of students who were given four quarters is 27 + 16 = 43.
4. Step 4: Calculate P(A ∩ B) and P(B). P(A ∩ B) is the probability of a student being given four quarters and spending the money, which is 27/43. P(B) is the probability of a student being given four quarters, which is also 43/total number of students.
5. Step 5: Substitute the values into the formula P(A|B) = P(A ∩ B) / P(B). Simplify the expression to find the conditional probability.

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 spending their money on gum given that they received four quarters. The formula for calculating 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 students purchasing gum, conditioned on the fact that they were given four quarters. This concept is crucial for understanding how the denomination of money influences spending behavior.

Data Interpretation

Data interpretation involves analyzing and making sense of data presented in tables or graphs. In this scenario, the table provides counts of students who purchased gum versus those who kept the money, which is essential for calculating the required probabilities. Understanding how to extract relevant information from data is key to answering statistical questions effectively.