Question

For three events $A,B$ and $C,P$(Exactly one of $A$ and $B$ occurs) $=P$(Exactly one of $B$ or $C$ occurs)$=P$(Exactly one of $C$ or $A$ occurs)$=\frac{1}{4}$ and $P$ (All the three events simultaneously )$=\frac{1}{16}$ the probability that at least one of the events ocurs is

• A. $\frac{7}{32}$
• B. $\frac{7}{16}$
• C. $\frac{7}{64}$
• D. $\frac{3}{16}$

Answer 1

Answer: (B)

$\frac{7}{16}$

P (A) + P (B) - 2P (A ∩ B) = 1/4

P (B) + P (C) - 2P (B ∩ C) = 1/4

P (A) + P (C) - 2P (A ∩ C) = 1/4

∑ P(A) - ∑ P (A ∩ B) = 3/8

P (A ∪ B ∪ C) = ∑ P(A) - ∑ P (A ∩ B) + P (A ∩ B ∩ C)

= 3/8 + 1/16

= 7/16