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. P(C)b. P(S)c. P(C and S)d. P(C | S)e. P(S | C)

Answer 1

Answer:

The probability that your friend had sprinkles given that he had chocolate $(P(S|C))$ is approximately 0.357 or 0.36 if you round it to 2 decimals.

Step-by-step explanation:

Let's define the following events:

C = "Your friends like chocolate flavor"

S = "Your friends like sprinkles topping"

We also know that $P(S) = 0.7$, $P(C) = 0.4$ and $P(S \cap C) = 0.25$. We are interested in the probability of given that your friend had chocalate what is the probability that he also likes sprinkles, in other words we want $P(S|C)$. Note that,

$P(S|C) = \frac{P(S \cap C)}{P(C)} = \frac{0.25}{0.70} \approx 0.357 \approx 0.36$