Multiple choice

A bag contains 3 white balls and 2 black balls, while another bag contains 5 white balls and 3 black balls. If a bag is chosen at random and a ball is drawn from it, what is the probability that it is white?

  1. 3/8

  2. 49/80

  3. 8/13

  4. 1/2
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B Correct answer
Explanation

P(Bag 1) = 1/2, P(White|Bag 1) = 3/5. P(Bag 2) = 1/2, P(White|Bag 2) = 5/8. Total P(White) = (1/2 * 3/5) + (1/2 * 5/8) = 3/10 + 5/16 = (24 + 25) / 80 = 49/80.

AI explanation

Using the law of total probability, the overall probability is the sum of the probabilities of choosing each bag and then drawing a white ball. The probability of choosing the first bag and drawing a white ball is 1/2 times 3/5, which equals 3/10. The probability of choosing the second bag and drawing a white ball is 1/2 times 5/8, which equals 5/16. Adding these gives 3/10 + 5/16 = 24/80 + 25/80 = 49/80. The probability is 49/80.

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