Question

Roll three dice A, B and C together. What is the probability that the numbers on A, B, C are strictly increasing or decreasing?

Answer 1

The Probability of strictly increasing or decreasing order is 20/216

Explanation:

First Die 1 2 3 4 5 6

Second Die 1 2 3 4 5 6

Third Die 1 2 3 4 5 6

Total number of outcomes= 6*6*6= 216

Possible outcomes of increasing order

1,2,3-----1,2,6 (4)

1,3,4------1,3,6 (3)

1,4,5------1,4,6 (2)

1,5,6 (1)

2,3,4—-2,4,6 (3)

2,4,5—-2,4,6 (2)

2,5,6 (1)

3,4,5—-3,4,6 (2)

3,5,6 (1)

4,5,6 (1)

Total number of possible moves of increasing order= 4+3+2+1+3+2+1+2+1+1= 20

Probability of strictly increasing order is 20/216

Similarly Probability of strictly decreasing order is calculated which is also equal to 20/216