In your sock drawer you have 4 blue, 5 gray, and 3 black socks. half asleep one morning you grab 2 socks at random and put them on. find the probability you end up wearing

This is a matter of probability and statistics. Probability is the study of calculating the chances or likelihood of an event occurring out of the total number of events. This likelihood is always presented as part of a whole. It could be in fractions or percentages.

For this problem, you have to designate the color of sock you end up wearing. I think your forgot to complete your question. In that case, let's just assume that you want to know the probability that you end up wearing two blue socks. You should not that in probability, when you are asked to find the probability of event A 'AND' event B happening, then you multiply their probabilities. In this case, the probability is

4/12 × 3/11

The first terms represents 4 blue socks out of 12 total socks. After that first random choice, your total socks would now be 11. Because you 'consumed' your original pool of choices, the next probability would change basing on the new pool of eliminated choices.

So, the total probability is 1/11 or 9.09%.