Box P has 2 red balls and 3 blue balls. Box Q has 3 red balls and 1 blue ball.…

GATE · 2005 · CS

Box P has 2 red balls and 3 blue balls. Box Q has 3 red balls and 1 blue ball. A ball is selected as follows:

(i) Select a box.
(ii) Choose a ball from the selected box, with each ball in that box equally likely to be chosen.

The probabilities of selecting boxes P and Q are 1/3 and 2/3, respectively. Given that the selected ball is red, what is the probability that it came from box P?

  1. A.

    4/19

  2. B.

    5/19

  3. C.

    2/9

  4. D.

    19/30

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