I found this problem in a book (relates to ML, $F_1$ and $F_2$ are supposed to be features and $C$ is supposed to be label)
Given:
- $P(F_1=T \mid C=T) = 0.8$
- $P(F_1=T \mid C=F) = 0.9$
- $P(F_2=T \mid C=T) = 0.4$
- $P(F_2=F \mid C=F) = 0.6$
- $P(C=T) = 0.4$
- Assume $F_1$, $F_2$ are independent
What is $P(C=T \mid F_1=T, F_2=T)$?
The answer should be $0.2831$ but I'm not sure how to arrive here. I know that $$P(C=T \mid F_1=T, F_2=T) = \frac{P(C=T \;\cap \;F_1=T\;\cap\;F_2=T)}{P(F_1=T\;\cap\;F_2=T)}$$ but I'm not sure where to go from there