There are 8 white and 6 black balls in the urn. Two balls are taken out of the urn at once.

There are 8 white and 6 black balls in the urn. Two balls are taken out of the urn at once. Find the probability that both balls will be white.

1) There are 8 + 6 = 14 balls in the urn
2) The total number of outcomes is the number of ways to select all combinations, regardless of the order, from 2 balls out of a total set of 14 balls, which is the number of combinations C from 14 to 2;
С = 14! / (2! · (14 – 2)!) = 13 · 14/2 = 91;
3) Now we find the number of all favorable outcomes. It is equal to the number of ways to choose 2 white balls out of 8 possible – these are combinations C1 from 8 to 2;
4) C1 = 8! / (2! (8 – 2)!) = 8 7/2 = 28;
The sought probability will be:
C1 / C = 28/91 = 0.308;
Answer: The probability that both balls taken out are white 0.308;