Question

probability and statistics
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 every day, what is
the probability that the person also buys cereal at least once a month?

Explanation:

Step1: Recall the formula for conditional probability

The formula for conditional probability is \(P(C|B)=\frac{P(B\cap C)}{P(B)}\). In terms of the Venn - diagram, \(P(B\cap C)\) is the number of elements in the intersection of \(B\) and \(C\), and \(P(B)\) is the number of elements in \(B\).

Step2: Identify the values from the Venn - diagram

The number of people who eat breakfast almost every day (\(B\)) is \(n(B)=11 + 53=64\) (the sum of the non - overlapping part of \(B\) and the overlapping part \(B\cap C\)). The number of people who eat breakfast almost every day and buy cereal at least once a month (\(B\cap C\)) is \(n(B\cap C) = 53\).

Step3: Calculate the conditional probability

Using the formula \(P(C|B)=\frac{n(B\cap C)}{n(B)}\), we substitute \(n(B\cap C) = 53\) and \(n(B)=64\). So \(P(C|B)=\frac{53}{64}\).

Answer:

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