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  4. Three balls are selected at random in order from a box containing 2 red, 3 yellow and 4 black balls. The probability that the third is yellow given that the first is red and the second is black and also that the balls are replaced after each selection is

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Q. Three balls are selected at random in order from a box containing 2 red, 3 yellow and 4 black balls. The probability that the third is yellow given that the first is red and the second is black and also that the balls are replaced after each selection is

Probability - Part 2

Solution:

Conditional probability that the third is yellow given that the first is red and the second is black is
$P ( A / B )=\frac{ P ( A \cap B )}{ P ( B )}=\frac{\frac{2}{9} \cdot \frac{4}{9} \cdot \frac{3}{9}}{\frac{2}{9} \cdot \frac{4}{9}}=\frac{1}{3}$