Answer :
If a dice is thrown n-times or n-dice are thrown simultaneously then the total number of outcomes = 6 × 6×6.....×6 (n - times) = 6n.
No. of total outcomes in throwing a dice for two times = 62 = .
| - | 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 |
(i) Let E be the event that 5 will not come up either time, then the favourable outcomes are =
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∴ P(E) =
No. of favourable outcomes
No. of total outcomes
=
(ii) Let E be the event that 5 will come up atleast once.=
No. of favourable outcomes =
∴ P(E) =No. of favourable outcomes
No. of total outcomes
=