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Question
Two dice are rolled simultaneously. What is the probability that 6 will come up at least once?
Options
`1/6`
`7/36`
`11/36`
`13/36`
Solution
`11/36`
Explanation:
| First dice | Second dice | ||||||
| 1 | 2 | 3 | 4 | 5 | 6 | ||
| 1 | (1, 1) | (1, 2) | (1, 3) | (1, 4) | (1, 5) | (1, 6) | |
| 2 | (2, 1) | (2, 2) | (2, 3) | (2, 4) | (2, 5) | (2, 6) | |
| 3 | (3, 1) | (3, 2) | (3, 3) | (3, 4) | (3, 5) | (3, 6) | |
| 4 | (4, 1) | (4, 2) | (4, 3) | (4, 4) | (4, 5) | (4, 6) | |
| 5 | (5, 1) | (5, 2) | (5, 3) | (5, 4) | (5, 5) | (5, 6) | |
| 6 | (6, 1) | (6, 2) | (6, 3) | (6, 4) | (6, 5) | (6, 6) | |
Total Number of outcomes = 36
Number of outcomes where 6 will come up at least once = 11
The probability that 6 will come at least once = `"Number of outcomes where 6 will come at least once"/"Total number of outcomes"`
= `11/36`
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