Probability Question

Probability Question

Question:

[x] = greatest integer less than equal to x. If x lies between 3 and 5. What is the probability than [x²] = [x]²?

A. Roughly 0.64

B. Roughly 0.5

C. Roughly 0.14

D. Roughly 0.36

Correct Answer: (C)

Explanation:

Let us take a few examples.

[3²] = [3]²

[3.5²] =12             [3.5]² = 9

[4²] = 16               [4]² = 16

For x Î (3, 5). [x]² can only take value 9, 16 and 25.

Let us see when [x²] will be 9, 16 or 25

If [x²] = 9,  x² [9, 10)

=> x[3, )

[x²] = 16 => x² [16, 17)

=> x [4, )

In the given range [x²] = 25 only when x = 5

So [x²] = [x]² when x [3, ] or [4, ) or 5.

Probability =

= = 0.14

Difficulty Level 2