Assume that removing a ball from bag **A** or bag
**B** is equally likely, the probability of choosing a
blue ball from bag **A** is 3/10 and the probability
of choosing a blue ball from bag **B** is 4/14 so the
probability of choosing a blue ball is 3/10 + 4/14 = 41/70.

Theoretically in 70 trials, 41 of the outcomes would give a blue
ball and 21 of these would of been drawn from bag
**A** . Given that the ball drawn was blue the
probability that it came from bag **A** is 21/41.

The only correct solution to date came from Matthew (Smithdon High School)