Question

There are 5 black balls and 10 red balls in an urn. If 3 balls are drawn without replacement, what is the probability that no black balls are drawn? Express your answer as a fraction or a decimal number rounded to four decimal places.

Answer 1

There are 5 black balls and 10 red balls in an urn. If 3 balls are drawn without replacement, the probability that no black balls are drawn is calculate as below.

As there are 5 black balls out of the total 15 balls in the urn, the probability of taking a black ball is 5/15 . So the probability of not getting a black ball is . So the probability that the first ball is not black is 10/15. Since we are taking ball without replacement, now there will be 14 balls in total and 9 non black balls. So the probability that the second ball is also not black is 9/14. Now there would be 13 balls in total and 8 non black balls. So the probability that the third ball is also not a black is 8/13. The final probability is the product of these three probabilities as the order of color of balls is not important. So the probability that no black balls are drawn is