Question

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

• A. $\frac{2}{5}$
• B. $\frac{4}{5}$
• C. $\frac{3}{5}$
• D. $\frac{1}{5}$

Answer 1

Answer: (A)

$\frac{2}{5}$

Answer 2

Let 5 horses are ${H1, H2, H3, H4}$ and ${H_5}$. Selected pair of horses will be one of the 10 pairs (i.e.; ${^5C_2} ): { H1 H2, H1 H3, H1 H4, H1 H5, H2 H3, H2 H4, H2 H5, H3 H4, H3 H5 }$ and ${H_4 H_5}$. Any horse can win the race in 4 ways. For example : Horses $H_2$ win the race in 4 ways ${H1 H2, H2 H3, H2 H4}$ and ${H2 H5}$. Hence required probability = $\frac{4}{10} = \frac{2}{5}$