Question

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 them wins the race.

Answer 1

Let Q, R, S and T be the events where horses A, B, C and D win the race, respectively.
Then, $P\left(Q\right)=\frac{1}{4},P\left(R\right)=\frac{1}{5},P\left(S\right)=\frac{1}{6}\mathrm{and}P\left(T\right)=\frac{1}{7}$
Since only one horse can win the race, Q, R, S and T are mutually exclusive events.
∴ Required probability = P (Q ∪ R ∪ S ∪ T)
= P(Q) + P(R) + P(S) + P(T)
= $\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+\frac{1}{7}$
= $\frac{319}{420}$