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 sprinkles (S) topping. The remaining do not like sprinkles. 25% of your friends like chocolate (C) and also like sprinkles (S). If your friend had chocolate, how likely is it that they also had sprinkles? (Note: Some answers are rounded to 2 decimal places).
A. 0.10
B. 0.18
C. 0.28
D. 0.36
E. 0.63

Answer 1

Answer: D. 0.36

Step-by-step explanation:

Given : 70% of your friends like chocolate (C).

i.e. P(C)=0.70

25% of your friends like chocolate (C) and also like sprinkles (S).

i.e. P(C∩S)=0.25

To find : your friend had chocolate, how likely is it that they also had sprinkles

Using  conditional probability formula , we have

$\text{P(likes Sprinkle|given that likes chocolate)}=P(S|C)=\dfrac{P(C\cap S)}{P(C)}\\\\=\dfrac{0.25}{0.70}\\\\=0.357142857143\approx0.36\ \ \text{[Rounded to 2 decimal places.]}$

Hence, the correct answer is D. 0.36