## How many socks do you need to take out of the drawer?

The answer is four. Although there are many socks in the drawer, there are only three colors, so if you take four socks then you are guaranteed to have at least one matching pair.

**What is the probability that the pair of socks taken 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.

**How do you find the probability of a sock?**

The probability of picking a pair of white socks is also 1/2 of 11/23, meaning in order to get the probability of picking any matching pair, you add these two together. The final probability of picking a matching pair of socks is 11/23, or 47.8 percent.

### What is the probability that two randomly selected socks have a different color?

From 10 socks you are choosing 2, so you have (102) possibilities. And to two socks to be different color you have to pick one blue and one white so you have (51)(51) possibilities. So the final result is 2545=59.

**What is the minimum number of socks taken to ensure that a pair of socks of the same color are selected?**

The answer is, of course, three socks. (The first two socks could match, but if not, the third sock is guaranteed to match one of the others). Above are all eight possible combinations of socks possible.

**How many socks do I have to take from the drawer to get at least 2 socks of the same color?**

In the worst case, you may pick 6 socks each of a different color. So in order to get at least two socks on the same color, you need to pick at least 7 socks. It’s a simple application of the Pigeon hole principle.

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

So the probability that the second sock is blue is 3/11 or 27%. The probability that the first and second socks are blue is the product of the two probabilities, about 9% (or 9 times out of 100). With decimal places, it’s 9.0909%.

**What is the probability that we take out two socks and that they are a matching pair?**

As there are 12 socks in total, and we are taking 2 of them, there would be 12C2 = 66 ways to do this. Of these 66 2-sock combinations, 6 of them would correspond to the matched pairs of socks. Therefore the probability of getting a matched pair would be 6/66 or 1/11 ( 0.090909…)

**What is the smallest number of socks you must take out of the drawer if there was a 40 watt bulb switched on in the room your answer?**

What is the smallest number of socks you must take out of the drawer in order to be certain that you have a pair that match? Solution: Three socks.

### What is the probability that the socks in the drawer will red?

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. So the probability that the pair will be red is the multiplication of the two: 1/5 X 1/9 = 1/45.

**How many socks are there in your sock drawer?**

“In your sock drawer there are 6 blue socks, 2 red socks and 2 white socks, distributed so that the probability of picking each is equal. Without looking, you draw one at put it to one side before drawing another at random.

**How to answer the famous probability interview question with pairs of socks?**

Let’s learn how to answer the famous probability interview question involving pairs of socks. There’s a famous interview question I’ve seen on the internet. It goes something like this: I have ‘x’ blue socks and ‘y’ red socks in a drawer. I take 2 socks from the drawer without looking.

## What is the effect of an unmatched Sock in a drawer?

The formula is eminently reasonable, for if any of the three numbers is $1,$ the effect of having an unmatched sock in a drawer is to increase the denominator without adding anything to the numerator. Solution 2