Question

If A and B are two events, the probability that at least one of them occurs is
(a) P(A) + P(B) – 2 P(A ∩ B)
(b) P(A) + P(B) – P(A ∩ B)
(c) P(A) + P(B) + P(A ∩ B)
(d) P(A) + P(B) + 2P(A ∩ B)

Answer 1

For two events A and B,
Probability that at least are of them occurs is$P\left(\overline{A}\cap B\right)+P\left(A\cap \overline{B}\right)$
$$\begin{gathered} =P\left(B\right)-P\left(A\cap B\right)+P\left(A\right)-P\left(A\cap B\right) \\ =P\left(A\right)+P\left(B\right)-2P\left(A\cap B\right) \end{gathered}$$
Hence, the correct answer is option A.