A pair of fair dice is rolled, and the sum of the two numbers falling uppermost is observed. The probability of obtaining a sum of 2 is the same as that of obtaining a 5 since there is only one way of getting a 2-namely, by each die showing a 1; and there is only one way of obtaining a 5-namely, by one die showing a 2 and the other die showing a 3. What is wrong with this argument?

Question

Rohan Moon

Mathematics

29 January, 10:43

A pair of fair dice is rolled, and the sum of the two numbers falling uppermost is observed. The probability of obtaining a sum of 2 is the same as that of obtaining a 5 since there is only one way of getting a 2-namely, by each die showing a 1; and there is only one way of obtaining a 5-namely, by one die showing a 2 and the other die showing a 3. What is wrong with this argument?

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Answers (1)

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Amiah Morgan · Answer 1

4+1 also make five!

Step-by-step explanation:

A Sum of five can be obtained if one die shows 1 and the other shows 4. So there is more than one way of obtaining a sum of 5. Hence the probability of obtaining a sum of 2 can't be same as that of obtaining a 5.