In a horse race,the odds in favour of three h | vedclass

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(B) The odds in favour of the three horses are $1:2$,$1:3$,and $1:4$.The probabilities of winning for the three horses are $P(A) = \frac{1}{1+2} = \fr

Vedclass · Accepted Answer

$\frac{47}{60}$

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(B) The odds in favour of the three horses are $1:2$,$1:3$,and $1:4$.The probabilities of winning for the three horses are $P(A) = \frac{1}{1+2} = \frac{1}{3}$,$P(B) = \frac{1}{1+3} = \frac{1}{4}$,and $P(C) = \frac{1}{1+4} = \frac{1}{5}$.Since these are mutually exclusive events (only one horse can win),the probability that one of the horses will win is the sum of their individual probabilities:$P(A \cup B \cup C) = P(A) + P(B) + P(C) = \frac{1}{3} + \frac{1}{4} + \frac{1}{5}$.Taking the least common multiple of $3, 4, 5$,which is $60$:$P = \frac{20 + 15 + 12}{60} = \frac{47}{60}$.

In a horse race,the odds in favour of three horses are $1:2$,$1:3$,and $1:4$. The probability that one of the horses will win the race is

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