There are 10 white and black balls in the urn. The probability that among two balls taken out of it at the same time

There are 10 white and black balls in the urn. The probability that among two balls taken out of it at the same time, both will be black, is 11/5. How many white balls are in the urn?

If there are x black balls in the urn, then the probability of drawing a black ball at the first extraction is x / 10, at the second – (x – 1) / 9.

The probability of black balls appearing with two extractions is:
P = x / 10 * (x – 1) / 9 = (x² – x) / 90.

By convention, this probability is 1/15. Let’s make the equation:
(x² – x) / 90 = 1/15;
(x² – x) / 90 – 6/90 = 0;
x² – x – 6 = 0;
D = 1 + 4 * 6 = 25;
x1 = (1 – 5) / 2 = – 2 – the number of balls cannot be negative.
x1 = (1 + 5) / 2 = 3.

Answer: there are 3 black balls in the urn.