C. Let $S$ represent the sample space of classrooms on UIC’s campus. Events are defined as follows:
$A$ = classroom remodeled/built within the last $5$ years
$B$ = classroom with a window(s)
$C$ = classroom without a projector
The following probabilities are known: $\textbf{P}(A) = 0.1$, $\textbf{P}(B) = 0.6$, $\textbf{P}(C) = 0.3$, $\textbf{P}(A\cap B) = 0.1$, $\textbf{P}(A\cap C) = 0$ and $\textbf{P}(B\cap C) = 0.2$.
i. Compute the probability $\textbf{P}(A\cap B\cap C)$.
ii. Compute the probability $\textbf{P}(A\cup B\cup C)$.
iii. Provide evidence, using the rules of probability, that you cannot find a classroom remodeled/built within the last $5$ years that doesn’t have a window.
For part i. Am i right to assume the formula is $\textbf{P}(A)\textbf{P}(B|A)\textbf{P}(C|A\cap B)$ if i am not mistaken. If so can someone show me how to figure out this part of the formula $\textbf{P}(C|A\cap B)$?