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


b. 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: Write the formula for conditional probability. Using the formula P(A|B) = P(A ∩ B) / P(B), we need to calculate the probability of 'kept the money' (A) and 'given four quarters' (B). P(A ∩ B) is the number of students who kept the money and were given four quarters divided by the total number of students, and P(B) is the number of students given four quarters divided by the total number of students.
4. Step 4: Calculate the individual probabilities. P(A ∩ B) = 16 / Total Students, and P(B) = 43 / Total Students. Substitute these values into the formula for conditional probability.
5. Step 5: Simplify the expression. The conditional probability P(A|B) = (16 / Total Students) / (43 / Total Students). Cancel out 'Total Students' in the numerator and denominator to simplify the fraction to P(A|B) = 16 / 43.

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 after being given 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 a student keeping the money, given that they received four quarters. This concept is crucial for understanding how the context of the situation influences the likelihood of different outcomes.

Data Interpretation

Data interpretation involves analyzing and making sense of data presented in tables or graphs. In this scenario, the data table summarizes the outcomes of students given different denominations of money. Understanding how to read and interpret this data is essential for calculating probabilities and drawing conclusions about the effects of the denomination on spending behavior.