B is the event that the second ball is red, and A is the event that the first ball drawn is red.
I understand why P(B/A) is 4/11 in this question, and why P(B) = 5/12 by the law of total probability, but this intuitive explanation below does not make sense to me.
"If no information is given on the
outcome of the first draw, there is no reason for the probability of second ball being red
to differ from 5/12."
What does this mean? In my thought process, if we know that a ball has been drawn without replacement, then doesn't that mean that the denominator of the probability of the second ball being red has already been reduced to 11? How does the 5/12 make sense in a without replacement context?
Best Answer
When you are not given any information about the first ball drawn, then you should expect each individual ball to have an identical chance to be the second ball drawn.
Five of the twelve are red.