Question

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

Answer 1

Answer:

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

Step-by-step 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=$\frac{10!}{3!7!}$ = 120 ways

So, $2x=2\times120=240$

Thus $z=1000-240=760$

So, the probability is = $\frac{760}{1000} = 0.76$

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