In a race, the odds in favour of horses A,B,C,D are 1:3, 1:4, 1:5 and 1:6 respectively. Find probability that one of the wins the race.

Question

Philoid · Accepted Answer

Given, odds in favour of A is

⇒

⇒ 1 – P(A) = 3P(A)

⇒ 4P(A) = 1 ⇒ P(A) = 1/4

Odds in favour of horse B is

⇒

⇒ 1 – P(B) = 4P(B)

⇒ 5P(B) = 1 ⇒ P(B) = 1/5

Odds in favour of horse C is

⇒

⇒ 1 – P(C) = 5P(C)

⇒ 6P(C) = 1 ⇒ P(C) = 1/6

Odds in favour of horse D is

⇒

⇒ 1 – P(D) = 6P(D)

⇒ 7P(D) = 1 ⇒ P(D) = 1/7

We have to find the probability that one of the horses win the race.

∵ only one horse can win the race ⇒ A ,B,C and D are mutually exclusive events.

We need to find P(A ∪ B ∪ C ∪ D).

∵ A ,B,C and D are mutually exclusive events.

∴ P(A ∪ B ∪ C ∪ D) = P(A) + P(B) + P(C) + P(D)

=

Hence,

probability that one of the horses win the race = 319/420