Question

Which of the following is false?

• A. $P (\phi) = 0 $
• B. For any three M.E. events A, B and C, one can have $P(A) = \frac{2}{3} , P(B) = \frac{1}{4}, P(C) = \frac{1}{6}$
• C. P (A+ B) = P (A) + P (B) - P (AB)
• D. $P (A^c)= 1 - P (A).$

Answer 1

Answer: (B)

In alternative we must have
P (A) + P (B) + P (C) $\le$ 1 as A, B and C are mutually exclusive events. Here,
P (A) + P (B) + P (C) = $\frac{2}{3} + \frac{1}{4} + \frac{1}{6}$. is greater than 1, which is not possible