Question

If a, b, c are mutually exclusive and exhaustive events, such that



3 p(a) = 2p(b) = 6p(c). Find p(aub) and p(buc).

Answer 1

Using those two facts, we know that: 
P(A or B or C) = P(A) + P(B) + P(C) = 1 

Let s express each in terms of P(B). First fact, we know P(A) = 2P(B), so: 
2P(B) + P(B) + P(C) = 1 

Next we know that 3P(C) = 2P(B), so we could also say P(C) = (2/3)P(B), so: 
2P(B) + P(B) + (2/3)P(B) = 1 

To simplify things, let s just use x = P(B): 
2x + x + (2/3)x = 1 

Combine like terms: 
3x + (2/3)x = 1 

Multiply both sides by 3: 
9x + 2x = 3 
11x = 3 
x = 3/11 

Answer: 
P(B) = 3/11 

Double-check: 
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 

Answer: 
P(B) = 3/11