Question

Bag I contains 4 red and 5 black balls and bag II contains 3 red and 4 black balls. One ball is transferred from bag I to bag II and then two balls are drawn at random without replacement from bag II. The balls so drawn are both found to be black. Find the probability that the transferred ball is black

Answer 1

The probability that the transferred ball was black is: ²⁵/₃₇ 

or approximately: 0.6757

I will write this up if anyone wants to see the work.