Discussion
Take two long dice (rectangular parallelepiped), each having four rectangular faces labelled as 2, 3, 5, and 7. If thrown, the long dice cannot land on the square faces and has 1/4 probability of landing on any of the four rectangular faces. The label on the top face of the dice is the score of the throw.
If thrown together, what is the probability of getting the sum of the two long dice scores greater than 11?
Answer: D
The probability is 3/16.
Each die shows 2, 3, 5 or 7 with probability 1/4, so there are \(4 \times 4 = 16\) equally likely outcomes. A sum greater than 11 needs at least 12:
- 5 + 7 = 12
- 7 + 5 = 12
- 7 + 7 = 14
Every other pair gives 10 or less (for example 3 + 7 = 10, 5 + 5 = 10). Three favourable outcomes out of 16 gives 3/16. 1/8 counts 5 + 7 and 7 + 5 as one outcome, 1/16 counts only 7 + 7, and 3/8 doubles the correct value.
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