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In the cafeteria there are two bags of doughnuts that look delicious. Each bag h

ID: 3021657 • Letter: I

Question

In the cafeteria there are two bags of doughnuts that look delicious. Each bag has 30 doughnuts. Bag A contains twice as many stale doughnuts as fresh ones. Bag B contains equal number of fresh doughnuts and stale doughnuts. Suppose we choose one of these bags at random and randomly select 13 of the doughnuts in this bag. Among the selected doughnuts, we replace each stale doughnut with a fresh one bought elsewhere. The doughnuts are then returned into the bag. Suppose that after selecting a bag and swapping the stale doughnuts, we end up with 35 of the doughnuts in the bag being fresh.

(a) If we have chosen bag A, what is the probability of finding 35 of the doughnuts being fresh

after swapping the stale doughnuts? What if we have chosen bag B?

(b) What is the probability that we have chosen bag B given the outcome of the swapping procedure above?

Explanation / Answer

a)

Probability = 3/5 * 1/3 = 1/5

What if we have chosen bag B?

Probability = 3/5 * 3/5 = 0.36

(b) What is the probability that we have chosen bag B given the outcome of the swapping procedure above?

Probability = (1/30) / (3/5) = 1/18

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