..
Joint Probability
Suppose we have two events $A$ and $B$. Joint probability is the probability of all possible pairs of the output. For example
- A, B
- B, A
- A, A
- B, B
| A=Red | A=Blue | P(B) | |
|---|---|---|---|
| B=Red | (2/3)(2/3)=4/9 | (1/3)(2/3)=2/9 | 4/9+2/9=2/3 |
| B=Blue | (2/3)(1/3)=2/9 | (1/3)(1/3)=1/9 | 2/9+1/9=1/3 |
| P(A) | 4/9+2/9=2/3 | 2/9+1/9=1/3 |
In the above example A is the first draw from an urn. B is the second draw