1996 AHSME Problems/Problem 16
Problem
A fair standard six-sided dice is tossed three times. Given that the sum of the first two tosses equal the third, what is the probability that at least one "2" is tossed?
Solution
The third toss cannot be , since the minimal sum on the other two tosses is .
If the third roll is , then the first two rolls must be .
If the third roll is , then the first two rolls must be or .
If the third roll is , then the first two rolls must be , , or .
If the third roll is , then the first two rolls must be , , , or .
If the third roll is , then the first two rolls must be , , , , or
There are possibilities for the three tosses. Of those possibilities, have a in the first two rolls, and has a in the third. Therefore, the answer is .
See also
1996 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 15 |
Followed by Problem 17 | |
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