Question

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

Answer 1

Answer:

0.76

Step-by-step explanation:

Answer 2

The probability is 0.76.

Explanation:

Let:

• the number of strictly increasing arrangements = X
• the number of strictly decreasing arrangements = Y
• 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 possibility is

the possibility is = 760/1000

the possibility is = 760/1000 = 0.76