You are a prisoner but you will be released if you draw a red marble from one of two jars. If you draw a yellow marble you will be in prison for life. You must place 10 red marbles and 10 yellow marbles in the jars (at least one marble in each jar) so that you maximize your probability of freedom. Determine your probability of being released.
P(freedom) = P(1st jar AND red) + P(2nd jar AND red)
You want to make the first jar to contain only red marbles so that if
you choose that jar, you will be free. And you want the the second jar
to be such that if you get it you will have the greatest probability
of getting a red marble. Since all the yellow marbles will be in the
second jar, you want the greatest possible number of red marbles in it,
so you'd want 9 reds in the 2nd jar and only 1 red marble in the first
jar. So you'd put 1 red in the first jar and the other 19 marbles in
the second jar.
P(freedom) = P(1st jar AND red) + P(2nd jar AND red) =
· + · =
Edwin