# Five horses are in a race. Mr. $\dpi{100} A$ selects two of the horses at random and bets on them. The probability that Mr. $\dpi{100} A$ selected the winning horse is Option 1) 3/5 Option 2) 1/5 Option 3) 2/5 Option 4) 4/5

As we learnt in

Probability of occurrence of an event -

Let S be the sample space then the probability of occurrence of an event E is denoted by P(E) and it is defined as

$P\left ( E \right )=\frac{n\left ( E \right )}{n\left ( S \right )}$

$P\left ( E \right )\leq 1$

$P(E)=\lim_{n\rightarrow\infty}\left(\frac{r}{n} \right )$

- wherein

Where n repeated experiment and E occurs r times.

Total number of ways of betting on two horses = $5C_{2}$

Number of ways that winning horse is selected = 4

Since, keeping one horse fixed, other horse can be selected in 4 ways.

Probability = $\frac{4}{^5C_{2}}\:=\frac{4}{10}\:=\frac{2}{5}$

Option 1)

3/5

This option is incorrect.

Option 2)

1/5

This option is incorrect.

Option 3)

2/5

This option is correct.

Option 4)

4/5

This option is incorrect.

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