Let event A be there is no homework for Paul and even B be the weather is nice. Assume A and B are independent.
Now let event C be play baseball. And Paul only plays baseball when there is no homework and the weather is nice.
- How to express C in term of A and B?
- Given C, what is the probability of B?
- Given $\bar{C}$, what is the probability of B?
- Are A and B conditionally independent given C?
- Are A and B conditionally independent given $\bar{C}$
Here is my thinking.
- C should be $A \times B $
- It should be 1 but I am not sure how to calculate it.
- $P(B|\bar{C}) = \dfrac{P(B)-P(A)P(B)}{1-P(A)P(B)}$
- Yes.
- No.