Question

Five horses are in a race. Mr. 'A' selected two horses randomly and bet on them. The probability that Mr. 'A' selected the winning horse is

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

Answer 1

The correct option is C $\frac{2}{5}$

In total there are $5$ horses.

Out of those Mr.A has to select $2$ horses.

This can be done in $5C_2=10$ ways.

Out of $5$ horses only $1$ horse wins.

Let us say Mr.A selected the winning horse.

He has to select one more horse so that his set has $2$ horses including winning horse. Thus out of $4$ he has to select $1$ horse.

The number ways to select is $4C_1=4$ ways.

Thus the probability of selecting winning horse is $\frac{4}{10}=\frac{2}{5}$

Probability of selecting winning horse is $\frac{2}{5}$.