Question

Roll a die 10 sided die 3 times. What is the probability that the sequence is strictly increasing or decreasing?

Answer 1

The probability of obtaining a sequence which is neither strictly increasing nor decreasing in 0.76.

Explanation:

We have 10 possible outcomes on a single throw.

So, outcomes in 3 throws =
`10^(3) =1000` outcomes.

Let x be the number of strictly increasing arrangements.

Let y be the number of strictly decreasing arrangements.

Let z be the number of outcomes that are neither strictly decreasing nor strictly increasing

So, we have
`x+y+z=1000`

If we look at a strictly increasing arrangement from the other/opposite side, it will look like a strictly decreasing arrangement.

So, x = y

Hence, we can say the final equation will be :

`2x+z=1000`

And for strictly increasing arrangements ,all 3 numbers will be different and it can be done in 10C3 ways.

10C3=
`(10!)/(3!7!)` = 120 ways

So,
`2x=2*120=240`

Thus
`z=1000-240=760`

So, the probability is =
`(760)/(1000) = 0.76`

Therefore, the probability of obtaining a sequence which is neither strictly increasing nor decreasing in 0.76.