Geometry

Question Analysis
This question requires calculating the probability of two distinct dependent events occurring in a specific order when candies are taken from a jar without replacement.
The main focus is on accurately computing the probabilities of each event based on the changing composition of candies in the jar.

Key Concept Explanation
As with all dependent - event probability problems, the outcome of the first draw affects the probabilities for the second draw.
Removing a candy of one flavor changes the total number of candies and the number of candies of the other flavor available for the next draw.

Step-by-Step Solution
Calculate the probability of taking a fruit - flavored candy on the first draw: There are 12 candies in total, and 7 are fruit - flavored.
So, .
Calculate the probability of taking a chocolate - flavored candy on the second draw given that a fruit - flavored candy was taken on the first draw: After removing one fruit - flavored candy, there are 11 candies left, and 5 of them are chocolate - flavored.
So, .
Use the multiplication rule for dependent events:

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