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

Answer 1

0.3333 = 33.33% of this group likes chocolate

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.

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) = (P(A \cap B))/(P(A)) = (0.05)/(0.15) = 0.3333`

0.3333 = 33.33% of this group likes chocolate