As, out of 3 events A,B and C only one can happen at a time which means no event have anything common.

∴ We can say that A , B and C are mutually exclusive events.

By definition of mutually exclusive events we know that:

P(A ∪ B ∪ C) = P(A) + P(B) + P(C)

According to question one event must happen.

This implies A or B or C is a sure event.

∴ P(A ∪ B ∪ C) = 1 …Equation 1

We need to find odd against C

Given,

Odd against A = 8/3

⇒

⇒

⇒ 8 P(A) = 3 – 3 P(A)

⇒ 11 P(A) = 3

∴ P(A) = …Equation 2

Similarly, we are given with: Odd against B = 5/2

⇒

⇒

⇒ 5 P(B) = 2 – 2 P(B)

⇒ 7 P(B) = 2

∴ P(B) = …Equation 3

From equation 1,2 and 3 we get:

P(C) = 1 - =

∴ P(C’) = 1 – (34/77) = 43/77

∴ Odd against C =