Bag A contains 3 white, 7 red balls and Bag B contains 3 white, 2 red balls. One bag is selected at random and a ball is drawn from it. The probability of drawing the ball from the bag A, if the ball drawn is white, is

Engineering

Mathematics

Total Probability Theorem and Bayes Theorem

Question

$\frac{1}{4}$

$\frac{1}{3}$

$\frac{3}{10}$

$\frac{1}{9}$

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$P (A / W) = \frac{P (A \cap W)}{P (W)}$

$= \frac{\frac{1}{2} \times \frac{3}{10}}{\frac{1}{2} \times \frac{3}{10} + \frac{1}{2} \times \frac{3}{5}}$

$= \frac{3}{3 + 6} = \frac{3}{9} = \frac{1}{3}$

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