# 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?

There are 10 black and 5 white balls in the bag, so the number of all favorable outcomes in the sample space is

n(S) = 10+5=15

Let A be the event of getting a black ball in the first draw. Hence the probability becomes

(as there are 10 black balls out of 15 balls)

Let B represents the event of getting a black ball in the second draw. Hence the probability becomes

(as there are 10 black balls and one black ball is already drawn in first draw so now there are total of 9 black balls)

Then the probability of all being black balls without replacement

Hence the required probability is

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