Q.An urn contains 10 black and 5 white balls. Two balls are drawn from the urn one after the other without replacement. Find the probability that both drawn balls are black.

Without replacement, multiply the probability of black on the first draw by the (updated) probability of black on the second draw, given the first was black.

Step 1. Urn has $10$ black $+5$ white $=15$ balls total.

Step 2. $P(\text{first ball black})=\dfrac{10}{15}=\dfrac23$.

Step 3. Given the first was black, $9$ black balls remain out of $14$ total: $P(\text{second black}\mid\text{first black})=\dfrac{9}{14}$.

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