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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.
Solution
Let Q, R, S and T be the events where horses A, B, C and D win the race, respectively.
Then,
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)
= \[\frac{1}{4} + \frac{1}{5} + \frac{1}{6} + \frac{1}{7}\]
= \[\frac{319}{420}\]
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