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# Did You Figure it Out? Get the Answer to the Riddle from E-News Issue No. 5, November 2018

2018-11-14

## How many pairs of black socks are in Paul‘s drawer? Paul has assorted pairs of white socks and black socks in his sock drawer.

In Paul's drawer are 11 pairs of white socks and an unknown number of pairs of black socks. If he blindly pulls two socks out of the drawer, there is a 15% probability that he will be holding a pair of white socks.

How many pairs of black socks are in Paul‘s sock drawer?

## Solution

X= number of socks (22 items are white socks)

The probability of getting a pair of white socks when making two selections is 15 %, thus P(white pair) = 0.15.

If P1 (white) is the probability of getting white sock on the first pull, and P2 (white) is the probability of pulling a white sock the second time, then following applies:

P1 (white) * P2 (white) = 0,15

With P1 (white) = 22 / x and P2 (white) = 21 / (x-1)

This can be illustrated with the following equation which we set equal to zero. Now, we solve the quadratic equation with the p-q-formula, using the variables p = - 1 and q = (22 * 21) / 0.15, and resolve into „x“. There are 56 socks and consequently 28 pairs of socks in Paul‘s drawer. Since we already know that 11 pairs are white socks, 17 pairs (28 – 11 = 17) of black socks remain in Paul’s drawer.

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