Question

For the three events A, B and C, P (exactly one of the events A or B occurs)= P(exactly one of the events C or A occurs)

= P (exactly one of the events B or C occurs) and P (all the three events occur simultaneously) = p², where 0 < p < $\frac { 1 } { 2 }$ . Then the probability of at least one of the three events A, B and C occurring is–

• A.
• B. $\frac { p + 3 p ^ { 2 } } { 4 }$
• C.
• D.

Answer 1

Answer: (A)

Answer 2

P_A + P_B = P_B + P_C = P_C + P_A = p, from first two P_A = P_C

From 2^nd and 3^rd relation P_B = P_A

\ P_A = P_B = P_C = $\frac { \mathrm { p } } { 2 }$

\ P (A Č B Č C) = S₁ –S₂ + S₃

= $\frac { 3 } { 2 }$ p – 0 + p² = $\frac { 3 p + 2 p ^ { 2 } } { 2 }$