I found this exercise online:
From the list of integers {11,12,13...20} you choose a random one. What is the probability that the chosen number is divisible by 2, under the condition that it is greater than 13.
So my logic was that:
$\Omega$ = {11,12,13,14,15,16,17,18,19,20}
A - numbers divisible by 2
B - numbers greater than 13
A = {12,14,16,18,20)
B = {14,15,16,17,18,19,20)
A$\cap$B = {14,16,18,20}
P(A$\cap$B) = 4/10
But the actual answer is:
P(A|B) = P(A$\cap$B) / P(B) = 4/7
I know this is conditional probability but it seems so counterintuitive to me that I can't wrap my head around it.
Can someone please explain to me the logic behind that?