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
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Answer 1

Answer:

10 power 3 out comes will appear

Answer 2

The probability is 0.76.

Explanation:

Let:

• the number of strictly increasing arrangements = X
• the number of strictly decreasing arrangements = Y
• the number of neither strictly decreasing nor strictly increasing = Z

Like this,

X+Y+Z=1000

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

Thus, X = Y

= 2X+Z=1000

For a strictly increasing arrangement, all three numbers must be distinct which can be done in 10C3 ways.

Z = 1000-(10C3) × 2

= 760

Hence, the Probability is

= 760/1000

= 0.76