Question

If the odds against winning a race of three horses are respectively $3:1,4:1$ and $5:1$, what is the probability that one of these horses will win?

Answer 1

We have,

In a race, If the odd against winning a race of three horses are respectively $3:1,4:1,5:1$.

Let the three horses $=A,B\text{and}C$

Now,

$P\left(A\right)=\frac{1}{3}$

$P\left(B\right)=\frac{1}{4}$

$P\left(C\right)=\frac{1}{5}$

These events are mutually exclusive.

That one of these horses will win$=P\left(A\right)+P\left(B\right)+P\left(C\right)$

$=\frac{1}{3}+\frac{1}{4}+\frac{1}{5}$

$\Rightarrow \frac{20+15+12}{60}$

$\Rightarrow \frac{47}{60}$

Hence, this is the answer.