There are 6 balls in the urn: 2 white and 4 black. Two balls are drawn at random.

There are 6 balls in the urn: 2 white and 4 black. Two balls are drawn at random. What is the probability that the drawn balls will be black?

In order to find the probability, you need to divide the number of variations of pulling out two black (!) Balls by the number of options to pull out any (!) Two balls.

We take the formula from combinatorics – C:

C = (number of black balls in general)! / ((number of balls taken at a time) * (number of black balls in general – (minus) number of balls at a time)!) = 4! / (2! * (4 – 2)! = 4!: (2! * 2!) = (1 * 2 * 3 * 4): (1 * 2 * 1 * 2) = 2 * 3 = 6 (variations pull out two black balls).

Now we find the number of variations to pull out any two balls, for this, in the first formula, simply change 4 to 6:

C = 6! / ((2!) * (6 – 2)!) = 6! / (2! * 4!) = (4! * 5 * 6) / (1 * 2 * 4!) = 5 * 3 = 15.

Accordingly, the probability of drawing two black balls out of the total is 6/15 or 2/5.

Answer: 2/5.