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,

\[P(Q) = \frac{1}{4}, P(R) = \frac{1}{5}, P\left( S \right) = \frac{1}{6} \text{ and }  P\left( T \right) = \frac{1}{7}\]

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)

                                      = \[\frac{1}{4} + \frac{1}{5} + \frac{1}{6} + \frac{1}{7}\]

                                      = \[\frac{319}{420}\]