(b) (−1/4, 1/3)
P(A) = (1 − 3p)/2
P(B) = (1 + 4p)/3
P(C) = (1 + p)/6
The events are mutually exclusive and exhaustive.
∴ P(A ∪ B ∪ C) = P(A) + P(B) + P(C) = 1
⇒ , ,
⇒ , ,
, ...(i)
...(ii)
and ...(iii)
The common solution of (i), (ii) and (iii) is .
∴ The set values of p are (1/4 , 1/3)