Question 325728: A pair of fair dice is rolled. Find the probability that the sum of the two numbers facing up is less than 10.
Found 2 solutions by stanbon, solver91311:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A pair of fair dice is rolled. Find the probability that the sum of the two numbers facing up is less than 10.
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Total number of sums: 36
# of 12's: 1
# of 11's: 2
# of 10's; 3
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# less than 10: 30
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P(sum < 10) = 30/36
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Cheers,
Stan H.
Answer by solver91311(24713)  (Show Source):
You can put this solution on YOUR website!
| Sum |
Ways |
# of Ways |
| 2 | 1,1 | 1 |
| 3 | 1,2; 2,1 | 2 |
| 4 | 1,3; 2,2; 3,1 | 3 |
| 5 | 1,4; 2,3; 3,2; 4,1 | 4 |
| 6 | 1,5; 2,4; 3,3; 4,2; 5,1 | 5 |
| 7 | 1,6; 2,5; 3,4; 4,3; 5,2; 6,1 | 6 |
| 8 | 2,6; 3,5; 4,4; 5,3; 6,2 | 5 |
| 9 | 3,6; 4,5; 5,4; 6,3 | 4 |
| 10 | 4,6; 5,5; 6,4 | 3 |
| 11 | 5,6; 6,5 | 2 |
| 12 | 6,6 | 1 |
The probability of anything is the number of ways that it can happen that you would consider a success divided by the number of ways it can happen total -- successes and failures.
If you add up the number of total ways that you can roll a pair of dice you get 36. There are 3 ways to get a ten, 2 ways to get an 11 and 1 way to get a 12, so there must be 36 minus 6 (3 plus 2 plus 1) ways to get less than 10.
John
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