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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 product of numbers appearing on the top of the dice is less than 9?
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 product of numbers appearing on the top of the dice is less than 9.
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 product of numbers appearing on the top of the dice is less than 9 are $(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (3, 1), (3, 2), (4, 1), (4, 2), (5, 1), (6, 1)$
Total number of favourable outcomes $=16$
Probability of an event $=\frac{Number\ of\ favourable\ outcomes}{Total\ number\ of\ possible\ outcomes}$
Therefore,
Probability that the product of numbers appearing on the top of the dice is less than 9 $=\frac{16}{36}$
$=\frac{4}{9}$
The probability that the product of numbers appearing on the top of the dice is less than 9 is $\frac{4}{9}$.
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