(solution) In the cafeteria there are two bags of doughnuts that look

(solution) In the cafeteria there are two bags of doughnuts that look

  1. 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 1/3 of the doughnuts in this bag. Among the selected doughnuts, we replace each stale doughnut with fresh doughnut after it has been selected. If the selected doughnut is fresh, we just put it back into the selected bag. Suppose that after selecting a bag and swapping the stale doughnuts, we end up with 3/5 of the doughnuts in the bag being fresh. 
    1. (a)  If we have chosen bag A, what is the probability of finding 3/5 of the doughnuts being fresh  after swapping the stale doughnuts? What if we have chosen bag B?
    2. (b)  What is the probability that we have chosen bag B given the outcome of the swapping procedure above?

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…