Difference between revisions of "1996 AHSME Problems/Problem 16"
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If the third die is <math>6</math>, then the first two dice must be <math>(1,5)</math>, <math>(2,4)</math>, <math>(3,3)</math>, <math>(4,2)</math>, or <math>(5,1)</math>. | If the third die is <math>6</math>, then the first two dice must be <math>(1,5)</math>, <math>(2,4)</math>, <math>(3,3)</math>, <math>(4,2)</math>, or <math>(5,1)</math>. | ||
− | There are <math>15</math> possibilities for the three dice. Of those possibiltiies, <math>7</math> have a <math>2</math> in the first two dice, and <math>1</math> has a <math>2</math> in the third die. Therefore, the answer is <math>\boxed{8}{15}</math>. | + | There are <math>15</math> possibilities for the three dice. Of those possibiltiies, <math>7</math> have a <math>2</math> in the first two dice, and <math>1</math> has a <math>2</math> in the third die. Therefore, the answer is <math>\boxed{\frac{8}{15}}</math>. |
==See also== | ==See also== | ||
{{AHSME box|year=1996|num-b=15|num-a=17}} | {{AHSME box|year=1996|num-b=15|num-a=17}} |
Revision as of 14:31, 19 August 2011
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 die cannot be , since the minimal sum on the other two dice is .
If the third die is , then the first two dice must be .
If the third die is , then the first two dice must be or .
If the third die is , then the first two dice must be , , or .
If the third die is , then the first two dice must be , , , or .
If the third die is , then the first two dice must be , , , , or .
There are possibilities for the three dice. Of those possibiltiies, have a in the first two dice, and has a in the third die. Therefore, the answer is .
See also
1996 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 15 |
Followed by Problem 17 | |
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 • 26 • 27 • 28 • 29 • 30 | ||
All AHSME Problems and Solutions |