# Brain Problem

Patrick Carney (pcarney@lunar.rutgers.edu)
Fri, 18 Apr 97 4:33:39 EDT

Hi-
Re your question " A jar contains one organ either a brain or a
heart. An Alien puts a brain in
the jar. He then pulls out a brain. What`s the probability that the jar
originally contained a brain. I think that this is the "LETS MAKE A DEAL"
problem and I feel that the answer is 2/3 but then sometimes I think it is
3/4?"
I believe the problem is from a book "The ALien's IQ Test" and this
particular question is one of about 1/2 dozen which are reprinted in the
April edition of Games Magazine.

Anyhow, I think that the cases are seen this way. Suppose the organ
already in is represented with an upper case letter and the new ione with a
lower case one. If it was originally a brain, the possibility is Bb. But if
it was a heart it is Hb. Now if he has picked up a brain, there are 3
possibilities or equal likelihood. He has B from the first leaving b. He has
b from the first leaving B or he has b from the second leaving H. Thus in 2
of the 3 possible cases in which he would draw out a brain, the original was
a brain. Only one would have the original a heart.

Take care.
Bro. Pat Carney