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The probability that the person also buys cereal at least once a month, given that a randomly chosen person eats breakfast almost every day is 53/64
What is random sample?
Random sample is the way to choose a number or sample in such a manner that each of the sample of the group has an equal probability to be chosen.
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 as,
- Circles B and C overlap.
- Circle B contains 11, circle C contains 4, and the intersection contains 53.
- Number 23 is outside of the circles.
Therefore, for circle B, it can be given as,
[tex]n(B)=11+53=64[/tex]
Similarly, for the circle C,
[tex]n(C)=53+4=57[/tex]
As the intersection of circle B and C contains 53,
[tex]n(BC)=53[/tex]
Now the probability that the person also buys cereal at least once a month, given that a randomly chosen person eats breakfast almost every day,
[tex]P(C|B)=\dfrac{P(BC)}{P(B)}\\P(C|B)=\dfrac{n(BC)}{n(B)}\\P(C|B)=\dfrac{53}{64}[/tex]
Hence, the probability that the person also buys cereal at least once a month, given that a randomly chosen person eats breakfast almost every day is 53/64
Learn more about the random sample here;
https://brainly.com/question/17831271
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