If there are 18 blue socks and 24 black socks what is the probability of pulling out 2 black socks?

18 + 24 = 42

first black sock = 24/42
second black sock = 23/41

product = 24/42 * 23/41 = .321

To find the probability of pulling out 2 black socks, we need to consider the total number of possible outcomes and the number of favorable outcomes.

Total number of socks = 18 (blue socks) + 24 (black socks) = 42

First, we need to select one black sock from the 24 black socks. So, the probability of selecting a black sock on the first pick is:

P(First pick is black) = Number of black socks / Total number of socks
= 24 / 42
= 12 / 21

After the first pick, we are left with 41 socks since we already selected one sock. Now, we need to select another black sock from the remaining 23 black socks. So, the probability of selecting a black sock on the second pick, given that the first pick was black, is:

P(Second pick is black | First pick was black) = Number of black socks / Total number of socks after the first pick
= 23 / 41

To find the probability of both events happening (selecting two black socks), we multiply the probabilities of the two picks:

P(Both picks are black) = P(First pick is black) * P(Second pick is black | First pick was black)
= (12 / 21) * (23 / 41)

Therefore, the probability of pulling out 2 black socks is (12 / 21) * (23 / 41).