Question

a survey asked about the number of people who eat breakfast almost every day (b) and the number of people who buy cereal at least once a month (c). the results of the survey are shown in the venn diagram. given that a randomly chosen person eats breakfast almost everyday, what is the probability that the person also buys cereal at least once a month? 11/64 11/53 53/64 53/57

Explanation:

Step1: Find the number of people who eat breakfast almost everyday

The number of people who eat breakfast almost everyday is \(11 + 53=64\) (the sum of the parts of set \(B\)).

Step2: Find the number of people who eat breakfast almost everyday and buy cereal at least once a month

The number of people who eat breakfast almost everyday and buy cereal at least once a month is \(53\) (the intersection part of \(B\) and \(C\)).

Step3: Use the formula for conditional probability

The formula for conditional probability \(P(C|B)=\frac{n(B\cap C)}{n(B)}\). Here, \(n(B\cap C) = 53\) and \(n(B)=11 + 53=64\).

Answer:

\(\frac{53}{64}\)