Given that we have three disjoint events, a,b,c and their probabilities are given as P(A), P(B), P(A ∪ B) etc, how can we find the probability of only two by three events occurring at one point?
2026-04-26 00:34:02.1777163642
probability of exactly two out of three events occuring
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Your answer has assumed that $A,B$ and $C$ are independent.
A more general formula would be $$p(A\cap B)+p(B\cap C)+p(C\cap B)-3p(A\cap B\cap C).$$
EXAMPLE
Consider throwing a die. Let $A$ be the event of getting a $6$, $B$ the event of getting a $5$ and $C$ the event of getting at least $5$.
The the probability of precisely two events occurring is $\frac{1}{3}$ whereas your formula gives $\frac{1}{9}$.