Difference between revisions of "2005 AMC 10B Problems/Problem 9"
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Revision as of 11:14, 4 July 2013
Problem
One fair die has faces 
, , 
, , 
, and another has faces 
, , 
, , 
, . The dice are rolled and the numbers on the top faces are added. What is the probability that the sum will be odd?
Solution
In order to obtain an odd sum, exactly one out of the two dice must have an odd number. We can easily find the total probability using casework.
Case 1: The first die is odd and the second die is even.
The probability of this happening is 
Case 2: The first die is even and the second die is odd.
The probability of this happening is 
Adding these two probabilities will give us our final answer. 
See Also
| 2005 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 8 |
Followed by Problem 10 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AMC 10 Problems and Solutions | ||
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