Top Puzzle 12: The Two-Dice Probability Puzzle | Puzzles for Interview - Interview Preparation PDF Download

Introduction

In this puzzle, we will learn how to find the probability of getting a specific product when two dice are thrown together.

Problem Statement

Two dice are thrown together. Find the probability that the product of the numbers on the top of the dice is 12 this

Solution

Possible Outcomes
When two dice are thrown at the same time, there are 36 possible outcomes.
These outcomes can be listed as follows:
(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).

Favourable Outcomes 
In this puzzle, we need to find the probability of getting a product of 12 on the top of the dice.
To do this, we need to find the favourable outcomes.
The possible outcomes where the product of the numbers on the top of the dice is 12 are (2,6), (3,4), (4,3), and (6,2).

Probability Calculation 
We can find the probability of getting a product of 12 on the top of the dice by dividing the number of favourable outcomes by the number of possible outcomes.
In this case, the number of favourable outcomes is 4 and the number of possible outcomes is 36.
Therefore, the probability of getting the product of the numbers as 12 on the top of the dice is 1/9.

Conclusion

The probability of getting a product of 12 on the top of two dice is 1/9. To find the probability of getting a product of 10, we need to repeat the above steps with the possible outcomes where the product of the numbers on the top of the dice is 10.