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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.

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MrRoyal

Answer:

[tex]Probability = 0.2470[/tex]

Step-by-step explanation:

Given

[tex]Black = 4[/tex]

[tex]White = 5[/tex]

[tex]Total = 9[/tex] i.e. 5 + 4

Required

Determine [tex]P(Black\ and\ White)[/tex]

In probability;

[tex]P(A\ and\ B) = P(A) * P(B)[/tex]

So:

[tex]P(Black\ and\ White) = P(Black) * P(White)[/tex]

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

[tex]P(Black\ and\ White) = \frac{n(Black)}{Total} * \frac{n(White)}{Total}[/tex]

[tex]P(Black\ and\ White) = \frac{4}{9} * \frac{5}{9}[/tex]

[tex]Probability = \frac{20}{81}[/tex]

[tex]Probability = 0.2470[/tex]

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