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 .