### 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

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

IIM CAT Preparation Tips

## Jul 26, 2013

### 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

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