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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 numbers obtained have a product less than 16?
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 numbers obtained have a product less than 16.
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 numbers obtained have a product less than 16 are $(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5),$
$(4, 1), (4, 2), (4, 3), (5, 1), (5, 2), (5, 3), (6, 1), (6, 2)$
Total number of favourable outcomes $=25$
Probability of an event $=\frac{Number\ of\ favourable\ outcomes}{Total\ number\ of\ possible\ outcomes}$
Therefore,
Probability that the numbers obtained have a product less than 16 $=\frac{25}{36}$
The probability that the numbers obtained have a product less than 16 is $\frac{25}{36}$.
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