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

Q :Let A,B and C be three mutually exclusive and Exhaustive events, then

P(B) ,if

$\frac{P(C)}{3}=\frac{P(A)}{2}=P(B)$

Solution:

1)We get according to given condition,

$P(C)= 3P(B) , P(A) = 2P(B)$

2) We know if A,B and C are mutually exclusive and Exhaustive events ,then

$P(A)+P(B)+P(C)=1 \\ => 2P(B) +P(B)+3P(B) = 1 \\ => 6P(B) = 1 \\ => P(B) = \frac{1}{6}$

Hence, Our desired Value is 1/6.

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