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

Question

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 (A)  (1/3) (B) (1/2) (C) (8/243) (D) none of these

Tardigrade Admin · Accepted Answer

Conditional probability that the third is yellow given that the first is red and the second is black is P ( A / B )=( P ( A ∩ B )/ P ( B ))=((2/9) ⋅ (4/9) ⋅ (3/9)/(2)9 ⋅ (4)9=(1/3)

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

$\frac{1}{3}$

$\frac{1}{2}$

$\frac{8}{243}$

none of these

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