Geometry

Question Analysis
This question focuses on calculating the probability of two successive dependent events.
The main focus is on correctly determining the probabilities of each draw as the number of stickers and their types change after the first draw, and then applying the multiplication rule for dependent events to find the combined probability of these two events.

Key Concept Explanation
Dependent events imply that the outcome of the first sticker draw affects the probabilities of the second draw.
Since the stickers are drawn without replacement, the total number of stickers and the number of stickers of each shape decrease with the first draw, which impacts the likelihood of drawing a particular shape of sticker on the second draw.

Step-by-Step Solution
Calculate the probability of drawing a star - shaped sticker on the first draw:
There are 7 star - shaped stickers out of 18 total stickers. So, .
Calculate the probability of drawing a heart - shaped sticker on the second draw given that a star - shaped sticker was drawn on the first draw:
After removing one star - shaped sticker, there are 17 stickers left, and 6 of them are heart - shaped. So, .
Use the multiplication rule for dependent events:

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