a survey asked about the number of people who eat breakfast almost every day (b) and the number of people…

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?\no $\frac{11}{64}$\no $\frac{11}{53}$\no $\frac{53}{64}$\no $\frac{53}{57}$

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?\no $\frac{11}{64}$\no $\frac{11}{53}$\no $\frac{53}{64}$\no $\frac{53}{57}$

Answer

Explanation:

Step1: Recall conditional - probability formula

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

Step2: Identify $n(B\cap C)$ and $n(B)$

From the Venn - diagram, $n(B\cap C) = 53$ (the number of elements in the intersection of B and C), and $n(B)=11 + 53=64$ (the number of elements in set B).

Step3: Calculate the probability

$P(C|B)=\frac{n(B\cap C)}{n(B)}=\frac{53}{64}$.

Answer:

$\frac{53}{64}$