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

Accepted Solution

Answer:The probability that your friend had sprinkles given that he had chocolate [tex](P(S|C))[/tex] 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 [tex]P(S) = 0.7[/tex], [tex]P(C) = 0.4[/tex] and [tex]P(S \cap C) = 0.25[/tex]. 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 [tex]P(S|C)[/tex]. Note that,[tex]P(S|C) = \frac{P(S \cap C)}{P(C)} = \frac{0.25}{0.70} \approx 0.357 \approx 0.36[/tex]