Question

An urn contains 4 black and 5 white balls. A ball is drawn at random and then replaced, and then a second ball is drawn. Find the probability that the first is black and the second iswhite.

Answer 1

`Probability = 0.2470`

Explanation:

Given

`Black = 4`

`White = 5`

`Total = 9` i.e. 5 + 4

Required

Determine
`P(Black\ and\ White)`

In probability;

`P(A\ and\ B) = P(A) * P(B)`

So:

`P(Black\ and\ White) = P(Black) * P(White)`

i.e. multiply the probability of selecting black by that of selecting white

`P(Black\ and\ White) = (n(Black))/(Total) * (n(White))/(Total)`

`P(Black\ and\ White) = (4)/(9) * (5)/(9)`

`Probability = (20)/(81)`

`Probability = 0.2470`