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) \(\frac{1}{5}\)

(b) \(\frac{2}{5}\)

(c) \(\frac{3}{5}\)

(d) \(\frac{4}{5}\)

Answer 1

(b) \(\frac{2}{5}\)

As each horse has equal chance of winning the race, Number of ways in which one of the five horses wins the race = ⁵C₁ 

∴ n(S) =⁵C₁  = \(\frac{|\underline5}{|\underline4|\underline1}\) 5

To find the chance that Mr A selects the winning horses, it is essential that one of the two horses selected by him wins the race. 

E : Mr A selecting the winning horse. 

⇒ n(E) = ²C₁ = 2 

∴ Required probability = \(\frac{n(E)}{n(S)}\) = \(\frac{2}{5}\).