Marbles and bags
Problem
Two bags contain different numbers of red and 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?
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Bag A 2 RED Image
3 BLUE Image
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Image
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Bag B 3 RED Image
4 BLUE Image
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Image
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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)