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?

\\(\frac{11}{64}\\)
\\(\frac{11}{53}\\)
\\(\frac{53}{64}\\)
\\(\frac{53}{57}\\)

Explanation:

Identify the given values from the Venn diagram

Using the Conditional Probability Calculation knowledge point

$$
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Calculate the total number of people who eat breakfast

Using the Conditional Probability Calculation knowledge point

$$ n(B) = n(B \setminus C) + n(B \cap C) = 11 + 53 = 64 $$

Calculate the conditional probability

Using the Conditional Probability Calculation knowledge point

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

Answer:

• (A) \(\frac{11}{64}\)
• (B) \(\frac{11}{53}\)
• (C) \(\frac{53}{64}\) (Correct answer)
• (D) \(\frac{53}{57}\)