Question

A box \(P\) contains 3 white and 7 red balls. A bag \(Q\) contains 4 green and 5 blue balls. Two balls are randomly drawn from box \(P\). If both are of the same color, one ball is drawn from bag \(Q\), and if the two balls are of different colors, 2 balls are drawn from bag \(Q\). If it is known that there is exactly one green ball among the balls drawn from bag \(Q\), then the probability that the two balls drawn from box \(P\) are of different colors is

• A. \(\frac{35}{67}\)
• B. \(\frac{21}{62}\)
• C. \(\frac{20}{43}\)
• D. \(\frac{32}{67}\)

Hint:

When a condition is given after an experiment, Bayes' theorem is usually the right approach. First calculate the conditional probabilities for the given event under each possible case, then update the probability accordingly.

Answer 1

The Correct Option is A