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 balls are black?

Explanation

Let A nad B denote, respectively, the events that first ball drawn is black and second ball drawn in white.
We have to find `P(AnnB) or P(AB).`
` P(AnnB)P(A)P(B//A)`
Now, P(A) =m P (black ball in first draw) `=10/15=2/3`
Also, given that the first ball drawn is black, i.e., event A has occurrred. Now, there are 9 black blalls and 5 white balls left in the urn. Therefore, the probability that the second ball drawn is white, given that ball in the first draw is black, is nothing but the conditional probability of B given that A has occurred.
`thereforeP(B//A)=5/14`
Therefore, `P(AnnB)=P(A)P(B//A)=2/3xx5/14=5/21.`