Discrete Math Probability Problem 3a Suppose you have a draw

Discrete Math Probability Problem-

3a. Suppose you have a drawer with B black socks and W white socks inside it (both B and W are greater than 0). Now, you draw out a sock at random and place it on the bed. Then you draw out a second sock at random and place it next to the first. Write an expression for the probability that both socks are black.

3b. What is the smallest possible number of socks in the drawer for which the probability in 3a is 0.5?

3c. Suppose we know that there are an even number of white socks. Now what is the smallest number of socks in the drawer for which the probability in 3a is 0.5?

Solution