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?
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.