Geometry

Question Analysis
This question involves calculating the probability of two consecutive dependent events of picking black socks from a drawer.
The main focus is on applying the concept of dependent - event probability to determine the likelihood of both events happening.

Key Concept Explanation
Dependent events mean that the result of the first sock pick changes the available options for the second pick.
As a sock is removed, the total number of socks and the number of black socks decrease, altering the probabilities for the second draw.

Step-by-Step Solution
Calculate the probability of picking a black sock on the first draw: There are 5 socks in total and 2 are black, so .
Calculate the probability of picking a black sock on the second draw given that a black sock was picked on the first draw: After removing one black sock, there are 4 socks left and 1 black sock remaining. So .
Use the multiplication rule for dependent events:

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