Question

If A, B, C are any three events and P(S) denotes the probability of S happening, then $P\{A\cap (B\cup C)\}=$

• A. $P\left(A\right)+P\left(B\right)+P\left(C\right)-P(A\cap B)-P(A\cap C)$
• B. $P\left(A\right)+P\left(B\right)+P\left(C\right)-P\left(B\right).P\left(C\right)$
• C. $P(A\cap B)+P(A\cap C)-P(A\cap B\cap C)$
• D. $P(B\cap C)+P(A\cap B)-P(A\cap B\cap C)$

Answer 1

Answer: (C)

$P(A\cap B)+P(A\cap C)-P(A\cap B\cap C)$

We have formula, given by,

$P\{A\cap (B\cup C\left)\right\}$

$=P(A\cap B)+P(A\cap C)-P(A\cap B\cap C)$