An urn contains 10 black and 5 white balls. Two balls are drawn from the urn one after the other without replacement. What is the probability that both drawn balls are black?
Question
An urn contains 10 black and 5 white balls. Two balls are drawn from the urn one after the other without replacement. What is the probability that both drawn balls are black?
Solution
To solve this problem, we need to understand that the probability of drawing a black ball changes after the first draw, because we are drawing without replacement.
Step 1: Calculate the probability of drawing a black ball on the first draw.
There are 10 black balls and 15 total balls, so the probability is 10/15 = 2/3.
Step 2: Calculate the probability of drawing a black ball on the second draw, given that a black ball was drawn on the first draw.
After drawing one black ball, there are now 9 black balls and 14 total balls, so the probability is 9/14.
Step 3: Multiply the probabilities from Step 1 and Step 2 to find the overall probability of drawing two black balls in a row.
The overall probability is (2/3) * (9/14) = 18/42 = 3/7.
So, the probability that both drawn balls are black is 3/7.
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