Multiple choice

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

  1. $ \displaystyle \frac{3}{5}$
  2. $ \displaystyle \frac{1}{5}$
  3. $ \displaystyle \frac{2}{5}$
  4. $ \displaystyle \frac{4}{25}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total ways to select 2 horses from 5 is 5C2 = 10. The number of ways to select the winning horse is 4C1 = 4 (the winner plus one of the 4 losers). The probability is 4/10 = 2/5.

AI explanation

The sample space consists of the 5C2 = 10 possible pairs of horses the man could select. The winning horse is included in exactly 4 of these pairs. Using the classical definition of probability, the chance is the number of favorable outcomes divided by the total outcomes, giving 4/10. This simplifies to 2/5.

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