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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 difference of the numbers appearing on the top of the two dice is 2?
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 difference of the numbers appearing on the top of the two dice is 2.
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 $n=36$
Outcomes, where the difference of the numbers appearing on the top of the two dice is 2 are $(1, 3), (2, 4), (3, 1), (3, 5), (4, 2), (4, 6), (5, 3), (6, 4)$
Total number of favourable outcomes $=8$
Probability of an event $=\frac{Number\ of\ favourable\ outcomes}{Total\ number\ of\ possible\ outcomes}$
Therefore,
Probability that the difference of the numbers appearing on the top of the two dice is 2 $=\frac{8}{36}$
$=\frac{2}{9}$
The probability that the difference of the numbers appearing on the top of the two dice is 2 is $\frac{2}{9}$.
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