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

Answer:

$Probability = 0.2470$

Step-by-step 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

$P(Black\ and\ White) = \frac{n(Black)}{Total} * \frac{n(White)}{Total}$

$P(Black\ and\ White) = \frac{4}{9} * \frac{5}{9}$

$Probability = \frac{20}{81}$

$Probability = 0.2470$