Question

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

• A. $\frac{3}{5}$
• B. $\frac{1}{5}$
• C. $\frac{2}{5}$
• D. $\frac{4}{25}$

Answer 1

Answer: (C)

$\frac{2}{5}$

Exactly one of the five horses will win.
The probability that $1st$ selected horse is losing horse is $\frac{4}{5}$
Now the probability that the $2nd$ selected horse from the remaining $4$ horse is a losing is $\frac{3}{4}$
Hence the probability that selected horse is losing horse is $\frac{4}{5}\times \frac{3}{4}=\frac{3}{5}$
So the required probability is $1-\frac{3}{5}=\frac{2}{5}$