Question

if you roll a 10-sided dice 3 times, what is the probability that they form neither a strictly increasing nor a strictly decreasing series?​

Answer 1

Answer:

Step-by-step explanation:

Let number of strictly increasing arrangements  be = X

Let number of strictly decreasing arrangements  be = Y

Let number of neither the strictly decreasing nor strictly increasing  be = Z

Thus ,

X+Y+Z=1000

A strictly increasing arrangement from the opposite side, will look like a strictly decreasing arrangement.

Thus, X=Y

= 2X+Z=1000

For a strictly increasing arrangement ,all the three numbers should be different which can be done in 10C3 ways.

Z = 1000- 10C3 × 2

= 760

Thus, the probability

= 760/1000

= 0.76

Answer 2

The probability forming neither increasing nor decreasing series is 0.76

Step-by-step explanation:

Assume the number of increasing the arrangements  be  X

Assume the number of decreasing the arrangements  be Y

Assume the number of neither decreasing nor increasing  be  Z

So,

X+Y+Z = 1000

Increasing arrangement from the opposite side, will look like for decreasing arrangement.

Therefore,

X=Y

So, Putting the Y in place of X

X + X + Z = 1000

2X+Z = 1000

For increasing the arrangement ,all the three numbers should be different which can be done in 10 C3 ways.

Z = 1000 - 10C3 × 2

= 760

Therefore , the probability

= Z/ 1000

= 760/1000

= 0.76

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