In a probability experiment, A, B and C are independent events. The probability that A will occur is r, the probability that B will occur is s, and the probability that C will occur is t whereas the r, s , and t are grater than zero.
Now I want to find a probability that, either A, B or C can occur but they can not occur together (like AAB or AAC is not allowed but AAA or BBB is allowed.)
In this case I used exclusion-inclusion formula to calculate the probability in this way:
$$P = P(A \cup B \cup C) - P(A\cap C) - P(B\cap C) -P(A\cap B) -P(A\cap B\cap C) $$
Is it a correct way?