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 Paradox? Not really (Posted on 2017-06-13)
Q1. What is the probability that the square of a random number from (0, 12) is greater than 36?

Q2. What is the probability that the square root of a random number
from (0, 144) is greater than 6?

Answer both question and comment upon the results.

 No Solution Yet Submitted by Ady TZIDON No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
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Q1:
let the random number be x, then we need
x^2>36
or
|x|>6
since (0,12) makes x positive then we need
x>6
thus the probability is
(12-6)/12=6/12=1/2

Q2:
again, let the random be x, then we need
sqrt(x)>6
x>36
thus the probability is
(144-36)/144=3/4

Comment:
I am assuming that the request for comment is in reference to the answers being different, which could seem counter-intuitive.  The simple explanation for this is because the transformation in Q1 (namely x^2) is not linear.

 Posted by Daniel on 2017-06-13 09:19:59

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