Two dice are thrown, find and number of outcomes.a)36b)6c)12d)None of ...
We know that in a single thrown of two die, the total number of possible outcomes is (6 × 6) = 36. Let S be the sample space. Then, n(S) = 36
When two dice are thrown, each die has 6 faces, numbered from 1 to 6. To find the total number of outcomes when both dice are thrown, you can use the multiplication principle.
- Outcomes for the first die: There are 6 possible outcomes (1, 2, 3, 4, 5, 6).
- Outcomes for the second die: Similarly, there are also 6 possible outcomes.
To find the total number of outcomes when both dice are thrown, multiply the number of outcomes for the first die by the number of outcomes for the second die:
Total Outcomes=Outcomes for the first die×Outcomes for the second die=6×6=36\text{Total Outcomes} = \text{Outcomes for the first die} \times \text{Outcomes for the second die} = 6 \times 6 = 36Total Outcomes=Outcomes for the first die×Outcomes for the second die=6×6=36
Conclusion
So, when two dice are thrown, there are a total of 36 possible outcomes. Each outcome can be represented as an ordered pair (x, y), where x is the result from the first die and y is the result from the second die. For example, (1, 1), (1, 2), ..., (6, 6).