Multiple choice

A pot contains 5 white and 3 red balls while another pot contains 4 white and 6 red balls. One pot is chosen at random and a ball is drawn from it. If the ball is white, what is the probability that it is from the first pot?

  1. 5/16

  2. 41/80

  3. 25/41

  4. 1/5

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

P(Pot1) = 1/2, P(White|Pot1) = 5/8. P(Pot2) = 1/2, P(White|Pot2) = 4/10 = 2/5. P(White) = (1/2 * 5/8) + (1/2 * 2/5) = 5/16 + 1/5 = (25+16)/80 = 41/80. P(Pot1|White) = (P(White|Pot1) * P(Pot1)) / P(White) = (5/16) / (41/80) = (5/16) * (80/41) = 25/41.

AI explanation

Using Bayes' theorem, the probability that the white ball came from the first pot is the probability of drawing from the first pot and getting white, divided by the overall probability of drawing a white ball. The numerator is 1/2 multiplied by 5/8, which equals 5/16, and the denominator is (5/16 + 1/2 * 4/10), which equals 5/16 plus 2/10 or 41/80. Dividing 5/16 by 41/80 gives 25/41.

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