Multiple choice

An urn contains 8 blue and 4 green balls. Two balls are drawn at random. The probability that both balls are of the same colour (all balls are considered to be different sizes)

  1. $\displaystyle \frac{17}{33}$
  2. $\displaystyle \frac{1}{33}$
  3. $\displaystyle \frac{14}{33}$
  4. $\displaystyle \frac{1}{11}$
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A Correct answer
Explanation

Total balls = 12. Ways to pick 2 = 12C2 = 66. Ways to pick 2 blue = 8C2 = 28. Ways to pick 2 green = 4C2 = 6. Total favorable = 28 + 6 = 34. Probability = 34/66 = 17/33.

AI explanation

The urn contains 8 blue and 4 green balls, giving a total of 12 balls. The number of ways to choose 2 balls of the same color is the sum of choosing 2 blue balls out of 8 and 2 green balls out of 4, calculated using combinations as 8C2 plus 4C2, which equals 28 plus 10 for a total of 38 favorable outcomes. The total number of ways to choose any 2 balls from 12 is 12C2, which equals 66. The required probability is 38/66, which simplifies to 17/33.

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