Suppose we have two bags of coins, both with 1p and 2ppieces.
One coin is taken from bag 1 and put into bag 2. Twocoins are then taken from bag 2. I want to find the probabilitydistribution for the value of coins taken from bag 2.
Theprobability that a 2p coin is taken from bag 1 is 3/5. If a 2p coinis taken from bag 1 and put into bag 2, it has 4 2p coins and 2 1pcoins.
We can then take from bag 2:
1p and 1p (=2p) with probability
1p and 2p (or 2p and 1p) (=3p) with probability
2p and 2p (=4p) with probability
We can put these values and probabilities in a table.
|
Value |
2p |
3p |
4p |
|
Probability |
2/30 |
16/30 |
12/30 |
Because the probability of taking a 2p coin from bag 1is 3/5 so all these probabilities are multiplied by 3/5.
|
Value |
2p |
3p |
4p |
|
Probability |
6/150 |
48/150 |
36/150 |
The probability that a 1p coin is taken from bag 1 is2/5. If a 1p coin is taken from bag 1 and put into bag 2, it has 3 2pcoins and 3 1p coins.
We can then take from bag 2:
1p and 1p (=2p) with probability
1p and 2p (or 2p and 1p) (=3p) with probability
2p and 2p (=4p) with probability
We can put these values and probabilities in a table.
|
Value |
2p |
3p |
4p |
|
Probability |
6/30 |
18/30 |
6/30 |
Because the probability of taking a 2p coin from bag 1is 3/5 so all these probabilities are multiplied by 3/5.
|
Value |
2p |
3p |
4p |
|
Probability |
12/150 |
36/150 |
12/150 |
The vales in the highlighted tables are then added togive the overall probability distribution.
|
Value |
2p |
3p |
4p |
|
Probability |
18/150 |
84/150 |
48/150 |