Hi there! I'm wondering if I've done the question below right ...
The teacher shows the students two bags. Bag A contains 3 gold coins and 2 silver coins. Bag B contains 4 gold coins and 5 silver coins. A coin is picked at random from Bag A and placed in Bag B. A coin is then picked at random from Bag B and placed in Bag A. These two operations are performed again in the same order. What is the probability that Bag A now contains five gold coins?
This is how I did it:
- In order to end up with 5 coins in A, each of the two swaps has to consist of putting gold coin into A from B and putting a silver coin into B from A.
- Probability of swaps occurring as described = probability of 1st swap x probability of 2nd swap = (4/9 x 2/5)(3/9 x 1/5) = 8/675
Does my logic follow? I'm curious to know as I've nowhere to check the answer!