I've been using this formula to get the answer:
$P (A \cup B \cup C) = P(A) + P(B) + P(C) - P(A \cap B) - P(A \cap C) - P(B \cap C) + P(A \cap B \cap C)$
Question:
If I'm right about using the formula above for this question, how can I do it step by step?
If I'm using a wrong formula, what's the right formula to use in this problem?
Here's the question/problem that I'm trying to solve so you can determine if I'm using the right formula:
A computer centre has three printers $A$, $B$, and $C$, which print at different speeds. Programs are routed to the first available printer. The probability that a program is routed to $A$, $B$, and $C$ are $0.3$, $0.2$, and $0.5$, respectively. Occasionally, a printer will jam and destroy a printout. The probabilities that printers $A$, $B$, and $C$ will jam are $0.01$, $0.05$, and $0.04$, respectively. Your program is destroyed when a printer jams.
1). What is the probability that your program will be destroyed?
this is conditional probability.
to get the probability, you need to find the summation of (probability of a preogram going throught the specifc printer) multiplied by the (probability of the jamming of that printer.
so the answer will be >(0.3)(0.01)+ (0.2)(0.05) +(0.5)(0.04) =0.033