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)
[9, 10)
=> x[3, 
)
[3, )
[x2]
= 16 => x2 [16, 17)
[16, 17)
=> x [4, 
)
[4, )
In
the given range [x2] = 25 only when x = 5
So
[x2] = [x]2 when x [3, ] or [4, ) or 5.
[3, ] or [4, ) or 5.
Probability = 
= 
= 0.14
= 0.14
Difficulty
Level 2