Multiple choice

An urn A contains 8 black and 5 white balls. A second urn B contains 6 black and 7 white balls.A blind folded persons is asked to draw a ball selecting one of the urns, the probability that the ball drawn is white is

  1. $\displaystyle \frac{5}{13}$
  2. $\displaystyle \frac{6}{13}$
  3. $\displaystyle \frac{7}{13}$
  4. $\displaystyle \frac{9}{13}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Probability of choosing Urn A = 1/2. Probability of white from A = 5/13. Probability of choosing Urn B = 1/2. Probability of white from B = 7/13. Total probability = (1/2 * 5/13) + (1/2 * 7/13) = 1/2 * (12/13) = 6/13.

AI explanation

Using the total probability theorem, the probability of selecting either urn is 1/2. Urn A has 5 white balls out of 13 total, and urn B has 7 white balls out of 13 total. The overall probability of drawing a white ball is (1/2 * 5/13) plus (1/2 * 7/13), which equals 12/26 or 6/13.

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