Probability of choosing a candy

Question

A jar contains 2 caramels, 7 mints and 16 dark chocolates. What is the probability of choosing a dark chocolate, eating it, then choosing a caramel?

Answer 1

These are dependent events, thus the outcome of one affects the outcome of the other. Therefore P(dark chocolate and then caramel) = P(dark chocolate) * P(caramel given 1 dark chocolate is gone)

D: eating a Dark Chocolate

C: eating a caramel

You might be more familiar with this type of formula: P(D and C) = P(D)*P(C|D)

P(D) = # of dark choc/total # of candies = 16/25

P(C|D) = # of caramel/total # of candies -1 = 2/24

Then we can multiply these probabilities together to find P(D and C) = 16/25 * 2/24 = 4/75 which is approximately .053 or 5.3%

I hope this helps!

Shannon L.