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

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
  1. $\frac{2}{5}$
  2. $\frac{4}{5}$
  3. $\frac{3}{5}$
  4. $\frac{1}{5}$

Solution

$\mathrm{n}(\mathrm{S})={ }^5 \mathrm{C}_2 ; \mathrm{n}(\mathrm{E})={ }^2 \mathrm{C}_1+{ }^2 \mathrm{C}_1$ $\mathrm{p}(\mathrm{E})=\frac{\mathrm{n}(\mathrm{E})}{\mathrm{n}(\mathrm{S})}=\frac{{ }^2 \mathrm{C}_1+{ }^2 \mathrm{C}_1}{{ }^5 \mathrm{C}_2}=\frac{2}{5}$

Asked in: JEE Main 2003

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