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Five horses are in a race. Mr. A selects two of the horses at random and on them. the probability that Mr. A selected the winning horse is

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Detailed Solution

Let 5 horses are $H_{1,} H_{2}, H_{3}, H_{4} and H_{5}$ total ways of selecting pair of horses be

$=^{5} C_{2} = [i.e. H_{1} H_{2}; H_{1} H_{3}; H_{1} H_{4}; H_{1} H_{5}] H_{2} H_{3}; H_{2} H_{4}; H_{2} H_{5}; H_{3} H_{5}; H_{4} H_{5}$

Favourable cases for each horse to win the race is 4 ways $(e.g.for H_{1} : H_{1} H_{2}, H_{1} H_{3}, H_{1} H_{4}, H_{1} H_{5})$

Hence required probability $\frac{4}{10} = \frac{2}{5}$

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