Question

Suppose your friends have the following ice cream flavor preferences: 70% of your friends like chocolate (C). The remaining do not like chocolate. 40% of your friends like sprinkles (S) topping. The remaining do not like sprinkles. 25% of your friends who like Chocolate (C) also like sprinkles (S). Of the friends who like sprinkles, what proportion of this group likes chocolate

Answer 1

The proportion of this group that likes chocolate is 0.625.

Explanation:

Conditional Probability

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

`P(B|A) = (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.

In this question:

Event A: Likes sprinkles

Event B: Likes chocolate

25% of your friends who like Chocolate (C) also like sprinkles (S).

This means that
`P(A \cap B) = 0.25`

40% of your friends like sprinkles (S) topping.

This means that
`P(A) = 0.4`

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

`P(B|A) = (P(A \cap B))/(P(A)) = (0.25)/(0.4) = 0.625`

The proportion of this group that likes chocolate is 0.625.