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# Did You Find Out? Get the Answer to the Riddle of E-News Issue No. 3, June 2016

2016-06-06

## 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, with a probability of 15%, he holds 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 selecting two times is 15 %, thus P(white pair) = 0.15.

If P1 (white) is the probability to get a white sock on the first pull, and P2 (white) is the probability to obtain a white sock on the second pull, then following applies:

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

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

This can be illustrated in the following equation which we transform in a way that a zero is left on one side.

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. As we know that 11 pairs are white socks, 17 pairs (28 – 11 = 17) of black socks remain in Paul’s drawer.

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