Question

If A and B are two events, then which of the following does not represent the probability that exactly one of A, B occurs is

• A. $P\left(A\right)+P\left(B\right)-P(A\cap B)$
• B. $P(A\cap B^{\prime })+P(A^{\prime }\cap B)$
• C. $P\left(A^{\prime }\right)+P\left(B^{\prime }\right)-2P(A^{\prime }\cap B^{\prime })$
• D. $P\left(A\right)+P\left(B\right)-2P(A\cap B)$

Answer 1

Answer: (A), (C)

The correct options are
A $P\left(A\right)+P\left(B\right)-P(A\cap B)$
C $P\left(A^{\prime }\right)+P\left(B^{\prime }\right)-2P(A^{\prime }\cap B^{\prime })$

$P\left(A\Delta B\right)=P\left(A\right)+P\left(B\right)-2P(A\cap B)$
Alternatively, $P\left(A\Delta B\right)=P(A\cap B^{\prime })+P(B\cap A^{\prime })$