Question

let a,b and c be three mutually and exhaustive events find p(b) if 1/3 p(c)=1/2 p(a)=p(b)

Answer 1

here is ur answer hope u will satisfied
p(a) +p(b) +p(c) = 1
p(a)=p(b) is given
we can write
p(b)+ p(b)+ p(c) = 1
2p(b) + 3/2 = 1. (1/3p(c)=1/2. p(c) = 3/2)
2p(b)= 1 - 3/2
2p(b) = - 1/2
p(b) = - 1/4

Answer 2

P(A or B or C) = P(A) + P(B) + P(C) = 1  

P(A) = 2P(B), so:  

2P(B) + P(B) + P(C) = 1  

 3P(C) = 2P(B),

P(C) = (2/3)P(B), so:  

2P(B) + P(B) + (2/3)P(B) = 1  

 x = P(B):  

2x + x + (2/3)x = 1  

3x + (2/3)x = 1  

9x + 2x = 3  

11x = 3  

x = 3/11  

P(B) = 3/11  

P(A) = 6/11  

P(B) = 3/11  

P(C) = 2/11  

P(A) = 2P(B) = 2*3/11  

P(A) = 3P(C) = 3*2/11  

The final Answer will be:

P(B) = 3/11