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.
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
(126)/12=6/12=1/2
Q2:
again, let the random be x, then we need
sqrt(x)>6
x>36
thus the probability is
(14436)/144=3/4
Comment:
I am assuming that the request for comment is in reference to the answers being different, which could seem counterintuitive. The simple explanation for this is because the transformation in Q1 (namely x^2) is not linear.

Posted by Daniel
on 20170613 09:19:59 