Multiple choice

There are two urns. One contains two white balls and four red balls, the other contains three white and nine red balls. All balls are of the same shape and size. From each urn, one ball is drawn. What is the probability of getting both the balls of the same colour?

  1. 1/24

  2. 7/12

  3. 1/12

  4. 1/2
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Urn 1: P(W)=2/6=1/3, P(R)=4/6=2/3. Urn 2: P(W)=3/12=1/4, P(R)=9/12=3/4. Same color = (P(W1)*P(W2)) + (P(R1)*P(R2)) = (1/3 * 1/4) + (2/3 * 3/4) = 1/12 + 6/12 = 7/12.

AI explanation

The probability of drawing two balls of the same colour is the sum of the probability of both being white and the probability of both being red. The probability of drawing a white ball from the first urn is 2/6 (or 1/3) and from the second urn is 3/12 (or 1/4), making the probability of both being white 1/3 times 1/4 = 1/12. The probability of drawing a red ball from the first urn is 4/6 (or 2/3) and from the second urn is 9/12 (or 3/4), making the probability of both being red 2/3 times 3/4 = 6/12 (or 1/2). Adding these gives 1/12 + 6/12 = 7/12. The probability is 7/12.

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