Multi-level Bayes


New Member
I guess that this is a multi level Bayes problem but there maybe a better technical name for it that I am not aware.

Three jars contain tokens of two different colors; red and green.
Jar A has 40% red and 60% green.
Jar B has 80% red and 20% green.
Jar C has 30% red and 70% green.
Two jars are selected at random and one token is taken from each jar.
The tokens are one red and one green.
What is the probability that the red token came from Jar B?
My solution:
Jar A: (1/3)x0.4x(1/2)x0.2x(1/2)x0.7 = 0.0046
Prob Jar A selected times prob. of red times prob. Jar B times green times
prob. Jar C times green.
Jar B: (1/3)x0.8 x (1/2)x0.6x(1/2)x0.7 = 0.0277
Jar C: (1/3)x0.3x(1/2)x0.6x(1/2)x0.2 = 0.003
Sum Jar A, Jar B, Jar C = 0.0353
p(B|red&green) = 0.0277/0.0353 = 0.785

Is this correct? Thanks in advance for any comments .


Ambassador to the humans
You're looking for P(red came from B | red and green showed up) which is different than P(B | red and green showed up).