Multiple choice

Bag A contains 2 white, 1 black and 3 red balls and bas B contains 3 black, 2 red and n white balls. One bag is chosen at random and 2 balls drawn from it at random, are found to be 1 red and 1 black. If the probability that both balls come from Bag A is 6/11 then n is equal to _______.

  1. 13

  2. 6

  3. 4

  4. 3
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The probability of drawing one red and one black ball from Bag A is 1/5. For Bag B, applying the given conditional probability requires the corresponding likelihood to be 1/6, which gives C(n + 5, 2) = 36. Hence n + 5 = 9 and n = 4.

AI explanation

Using Bayes' theorem, the probability that Bag A is chosen given the outcome is equal to the probability of the outcome from Bag A divided by the total probability of the outcome from both bags. The probability of drawing 1 red and 1 black ball from Bag A is (3C1 times 1C1) divided by 6C2, which is 3/15 or 1/5; accounting for the initial half chance of picking Bag A, this path contributes 1/10 to the total probability. The probability of the same outcome from Bag B is (2C1 times 3C1) divided by the quantity 5 plus n choose 2; accounting for the half chance of picking Bag B, this path contributes 6 divided by the quantity (5 plus n) times (4 plus n). Setting the equation where 1/10 divided by the sum of 1/10 and this second probability equals 6/11 allows us to solve for n, yielding 4.

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