I have 6 pairs of socks lying unmatched in my dresser drawer. Each pair is a different color(brown, black, red, yellow, green, and purple). When I wake up in the morning, I randomly grab 2 of the loose socks and put them on without looking. If 2 socks are randomly selected from the drawer, what is the probability that they match?

Thanks!

There are 36 different pairs of sox I could take,

of those 6 pairs will match,
The prob of picking a matching pair is 6.36 = 1/6

(This question is identical to this one:
Throw 2 dice, what is the prob of getting the same number on both? )

To find the probability of selecting a matching pair of socks, we need to determine the total number of possible outcomes and the number of favorable outcomes.

Total number of possible outcomes:
When we select 2 socks randomly, there are a total of C(12, 2) or 12 choose 2 ways to do so. This is because we have 12 socks (6 pairs) to choose from, and we want to select 2 of them. The formula for finding the number of combinations, denoted as C(n, r), is given by n! / (r! * (n-r)!), where n is the total number of possibilities, and r is the number of selections.

Number of favorable outcomes:
Since we want to select a matching pair, we need to pick 2 socks of the same color. There are 6 pairs in total, and for each pair, we have 2 options to select a sock. Therefore, the number of favorable outcomes is 6 * 2 = 12.

Now, we can calculate the probability using the formula:
Probability = Number of favorable outcomes / Total number of possible outcomes

Probability = 12 / C(12, 2)

To calculate C(12, 2), we can apply the formula:
C(12, 2) = 12! / (2! * (12-2)!)

Therefore, the total number of possible outcomes is: 12! / (2! * 10!) = (12 * 11) / (2 * 1) = 66

Now, we can substitute the values into the probability formula:
Probability = 12 / 66 = 2 / 11

Hence, the probability of picking a matching pair of socks is 2/11.