There are 10 balls in the urn: 3 white and 7 black. Two balls are taken out of the urn at once.

There are 10 balls in the urn: 3 white and 7 black. Two balls are taken out of the urn at once. What is the probability that both balls will turn out to be white?

The number N of all equally probable test outcomes is equal to the number of ways in which two balls can be removed from 10 balls, i.e., the number of combinations of 10 elements of 2 each:

N = C from 10 to 2 = factorial 10! / 21! (10 – 2)! = 45;

Number of Favorable Outcomes:

M = C from 3 to 2 = factorial 3! / 2! (3-2)! = 3;

Therefore, the desired probability is:

p = M / N = 3/45 = 1/15.