What is the probability that you get a pair of red socks?

Option A: you get a pair of red socks. There are 10 socks in the drawer, and 2 are red. Therefore the probability that the first one will be red is 2/10 = 1/5. Assuming that, the probability that the second will be red is 1/9 as there will only be 1 red left among the remaining 9.

How many socks must he take out to be sure that he has at least two black socks?

three socks
By the pigeonhole principle, the answer is 3. If three socks are taken from the drawer, at least two must have the same color. On the other hand two socks are not enough, because on might be brown and the other black.

How many colors of socks are in a sock drawer?

A sock drawer contains 5 different colors of socks. It has 20 white, 10 black, 10 gray, 6 red, and 4 purple. If you reach into the drawer and choose a sock randomly, what is the probability you will get a black sock?

What is the probability of drawing 2 socks from the drawer?

For each set of socks, there are 8. 8 * 7 (7 other socks to each being matched) = 56 possible combinations in each set of socks / 2 to remove duplicates = 28 possible combinations of socks in each set. 28 / 780 = 0.036 probability of drawing a pair when drawing 2 socks from the drawer. Cheers guys!

How many pairs of socks can you pick out of?

You can first find the probability of picking, say, a pair of red socks, then multiplying that probability by 3 because you can have 3 possible pairs of socks (with the same color). Another way of solving this is by finding the amount of possibilities with 2 socks of the same color divided by the total amount of possibilities.

How to pull two matching socks in 3 draws?

To pull two matching socks in three draws. you can pull 3 socks of the same color, or 2 socks of one color, and sock of annother color. $\\frac{5{4\\choose2}*16 + 5*{4\\choose3} }{20\\choose3}$ we can keep going with this methodolgy to work up to 4 and 5 4 draws.