An urn contains 4 white balls and 10 black balls Balls are s

An urn contains 4 white balls and 10 black balls. Balls are selected at random, and without replacement from this urn. What is the probability that the first black ball drawn comes in the third draw?

Solution

the urn contains 4 white balls and 10 black balls. balls are selected at random ans without replacement from this urn. so the draws are independent. there are all total 14 balls

P[ first balck ball comes in the third draw]=P[a white ball comes at the first draw from 14 balls]*P[ a white ball comes from the remaining 13 balls with 10 black and 3 white balls]*P[ a black ball comes from the remaining 12 balls with 10 black and 2 white balls]=(4/14)*(3/13)*(10/12)=0.05494 [answer]