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A black die and a white die are thrown at the same time. Write all the possible outcomes. What is the probability that the sum of the numbers appearing on the top of the dice is less than or equal to 12?
Given:
A black die and a white die are thrown at the same time.
To do:
We have to write all the possible outcomes and find the probability that the sum of the numbers appearing on the top of the dice is less than or equal to 12.
Solution:
When two dice are thrown, the total possible outcomes are $6\times6=36$.
All the possible outcomes are $(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4),$
$(2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1),$
$(5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)$
This implies,
The total number of possible outcomes $n=36$
All the possible outcomes appearing on the top of the dice have a sum less than or equal to 12.
Total number of favourable outcomes $=36$
Probability of an event $=\frac{Number\ of\ favourable\ outcomes}{Total\ number\ of\ possible\ outcomes}$
Therefore,
Probability that the sum of the numbers appearing on the top of the dice is less than or equal to 12 $=\frac{36}{36}$
$=1$
The probability that the sum of the numbers appearing on the top of the dice is less than or equal to 12 is $1$.
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