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. $\dfrac{4}{5}$
B. $\dfrac{3}{5}$
C. $\dfrac{1}{5}$
D. $\dfrac{2}{5}$

Answer 1

Hint: We first define the events of universal choice and the conditional choice of Mr. A selecting two of the horses at random and betting on them. We find the number of choices of those events happening. Then from the formula of basic probability $P\left( A \right)=\dfrac{n\left( A \right)}{n\left( S \right)}$, we find the probability of Mr. A selecting the winning horse.

Complete step-by-step solution:
There are five horses in a race. At least one of those five horses will win. The chances of 1 horse winning are $\dfrac{1}{5}$. If S be the event with the total number of choices then $n\left( S \right)=5$.
Now we assign the event of Mr. A selecting two of the horses at random and betting on them as event A. So, $n\left( A \right)=2$.
We need to find the probability of winning the race for Mr. A which is equal to the probability of event A happening.
So, $P\left( A \right)=\dfrac{n\left( A \right)}{n\left( S \right)}=\dfrac{2}{5}$. The probability that Mr. A selected the winning horse is $\dfrac{2}{5}$.
The correct option is D.

Note: We also could have used the probability of a horse winning the race. The probability of 1 horse winning is $\dfrac{1}{5}$. Mr. A chose 2 of them and these are exclusive events. So, the total probability would be $\dfrac{1}{5}+\dfrac{1}{5}=\dfrac{2}{5}$.