Marbles and bags
Two bags contain different numbers of red and blue marbles. A marble is removed from one of the bags. The marble is blue. What is the probability that it was removed from bag A?
Problem
Bag A contains 2 red and 3 blue marbles:
🔴🔴🔵🔵🔵
Bag B contains 3 red and 4 blue marbles:
🔴🔴🔴🔵🔵🔵🔵
A marble is removed from one of the bags. It is not known from which bag.
The marble is blue. What is the probability that it was removed from bag A?
Student Solutions
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)