1997 AHSME Problems/Problem 10
Problem
Two six-sided dice are fair in the sense that each face is equally likely to turn up. However, one of the dice has the replaced by and the other die has the replaced by . When these dice are rolled, what is the probability that the sum is an odd number?
Solution
On the first die, the chance of an odd number is , and the chance of an even number is .
On the second die, the chance of an odd number is , and the chance of an even number is .
To get an odd sum, we need exactly one even and one odd.
The odds of the first die being even and the second die being odd is
The odds of the first die being odd and the second die being even is .
The overall probability is , and the answer is .
See also
1997 AHSME (Problems • Answer Key • Resources) | ||
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