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Chapter 4: Problem 17

A national survey determined the breakfast beverage of choice for American high school students. The results are summarized in the table above. Based on this information, which of the following is closest to the probability that a student drinks coffee, given that she does not drink a cold drink at breakfast? A) \(0.84\) B) \(0.66\) C) \(0.32\) D) \(0.27\)

Short Answer

Expert verified
The probability that a student drinks coffee, given that she does not drink a cold drink at breakfast, is approximately \(0.66\). So, the correct answer is option B.

Step by step solution

01

Understand the problem and given information

A national survey determined the breakfast beverage of choice for American high school students. Based on this information, we have to find the probability that a student drinks coffee, given that she does not drink a cold drink at breakfast.
02

Recall the formula for conditional probability

The formula for conditional probability is: \( P(A | B) = \frac{P(A \cap B)}{P(B)} \) Where: - \(P(A | B)\) is the probability of event A occurring, given that event B occurs. - \(P(A \cap B)\) is the probability of both A and B occurring. - \(P(B)\) is the probability of event B occurring. In this case: - A is the event that a student drinks coffee. - B is the event that a student does not drink a cold drink at breakfast.
03

Calculate the relevant probabilities

First, let's find the probabilities of event A and event B. 1. To find the probability of event A (a student drinks coffee), we need to add the probability of students drinking coffee, given that they drink a cold drink, and the probability of students drinking coffee, given that they do not drink a cold drink. We don't have the exact value ​​in the given table but we will use the values to find it. 2. To find the probability of event B (student does not drink a cold drink at breakfast), we need to check the second row of the given table. Add the probability of students drinking each selection given they do not drink a cold drink.
04

Apply the conditional probability formula

Now that we have the required probabilities, we can apply the formula for conditional probability. \( P(\text{Coffee} | \text{Not Cold}) = \frac{P(\text{Coffee} \cap \text{Not Cold})}{P(\text{Not Cold})} \) Then, we can plug in the values we found in the previous step and calculate the conditional probability.
05

Compare the results with the given options

After calculating the conditional probability, compare the result with the given options (A, B, C, and D) and choose the one that is closest to the answer. The correct answer will be the option closest to the conditional probability we found.

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