Multiple choice

A bag contains 5 square boxes and 7 cylindrical boxes. Two boxes are drawn at random. Find the probability that they are the same shape.

  1. 31/66

  2. 21/66

  3. 11/66

  4. 1/5

  5. 31/61
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A Correct answer
Explanation

Total boxes = 12. Ways to choose 2 = 12C2 = 66. Ways to choose 2 square = 5C2 = 10. Ways to choose 2 cylindrical = 7C2 = 21. Total favorable = 10 + 21 = 31. Probability = 31/66.

AI explanation

The total number of ways to draw 2 boxes from the 12 available is 12C2, which equals 66. The number of ways to draw two square boxes is 5C2 (10 ways), and the number of ways to draw two cylindrical boxes is 7C2 (21 ways). The probability of getting the same shape is the sum of these successful outcomes divided by the total outcomes, or 31 divided by 66.

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