Answer:
A. 0.36 ; B. 0.72
Step-by-step explanation:
Probability of A, B, C, D to win the interview = P(A), P(B), P(C), P(D)
Given : P(A) = 2 P(B) ∴ P(B) = P(A) / 2
P(B) = 2/3 P(C) ∴ P(C) = 3/2 P(B) ∴ P(C) = 3/2 [P(A) / 2 ]
So, P(C) = 3/4 P(A)
P(C) = 1.5 P(D) ∴ P(C) = 3/2 P(D) ∴ P(D) = 2/3 P(C)
∵ P(C) = 3/4 P(A) ∴ P(D) = 2/3 [3/4 P(A)]
So, P(D) = 1/2 P(A)
Either of them will definitely win the interview. So probability of A or B or C or D winning = 1
So, P(A) + P(B) + P(C) + P(D) = 1
Putting above values : P(A) + P(A) / 2 + 3/4 P(A) + 1/2 P(A) = 1
P(A) [1+ 1/2 + 3/4+ 1/2] = [(4+2+3+2) /4] P(A)
∴ 2.75 P(A) = 1
So, P(A) = 1/2.75 = 0.36
P(B) = P(A)/2 = 0.36 /2 = 0.18
P(C) = 3/4 P(A) = 0.36 (3/4) = 0.27
P(D) = P(A)/2 = 0.36 /2 = 0.18
A. Probability A wins election = 0.36
B. Probability C doesn't win election = Pr A or B or D win election
= Pr (A) + Pr (B) + Pr (D) = 0.36 + 0.18 + 0.18 = 0.72
