The urn contains 5 white and 6 black balls. Find the probability that there are two white balls
The urn contains 5 white and 6 black balls. Find the probability that there are two white balls among the three randomly drawn balls.
There are 5 + 6 = 11 balls in the urn. By condition, you need to calculate the probability of taking out two white balls out of three. Obviously, the third ball is black.
Probability to take out the white ball:
P = 5/11;
The probability of taking out another white ball, while one white has already been taken out:
P = 4/10;
Probability to take out the black ball:
P = 6/9, because the black balls are still in the urn, and the total number of balls has been reduced to 9 pieces.
Multiplying these probabilities, we find the desired total probability of getting two white and one black balls out of the urn:
P = (5/11) * (4/10) * (6/9) = 4/33 = 0.12.
The order in which the balls are removed does not affect the result.
Answer: 0.12.