Suppose your friends have the following ice cream preferences: 31% of your friends like chocolate (C). The remaining do not like chocolate.

Question

Suppose your friends have the following ice cream preferences: 31% of your friends like chocolate (C). The remaining do not like chocolate. 15% of your friends like sprinkles (S) topping. The remaining do not like sprinkles. 5% of your friends like Chocolate (C) and also like sprinkles (S). Of the friends who like sprinkles, what proportion of this group likes chocolate

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Verity 5 years 2021-07-20T09:37:13+00:00 1 Answers 21 views 0

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  1. diemkieu
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    2021-07-20T09:38:57+00:00
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    Answer:

    0.3333 = 33.33% of this group likes chocolate

    Step-by-step explanation:

    Conditional Probability

    We use the conditional probability formula to solve this question. It is

    P(B|A) = \frac{P(A \cap B)}{P(A)}

    In which

    P(B|A) is the probability of event B happening, given that A happened.

    P(A \cap B) is the probability of both A and B happening.

    P(A) is the probability of A happening.

    Of the friends who like sprinkles, what proportion of this group likes chocolate:

    So,

    Event A: Likes sprinkles

    Event B: Likes chocolate

    15% of your friends like sprinkles (S) topping.

    This means that P(A) = 0.15

    5% of your friends like Chocolate (C) and also like sprinkles (S).

    This means that P(A \cap B) = 0.05

    So

    P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.05}{0.15} = 0.3333

    0.3333 = 33.33% of this group likes chocolate

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