NIMCET 2016 — Mathematics PYQ

Concept:
P(A) is the probability of an event “A”  
$P(A)=\frac{n(A)}{n(S)}$

Where $n(A)$ is the number of favourable outcomes and $n(S)$ is the total number of events in the sample space.

Calculations:
Given, there are 5 horses say H₁, H₂, H₃, H₄, H₅  
Mr. A selects two of the horses at random and bets on them.

Selection of horses can be done  
= H₁H₂, H₁H₃, H₁H₄, H₁H₅, H₂H₃, H₂H₄, H₂H₅, H₃H₄, H₃H₅, H₄H₅  
= 10 ways.

Only one horse (say H₃) can win  
= H₁H₃, H₂H₃, H₃H₄, H₃H₅ = 4 ways.

The probability that Mr. A selected the winning horse is  
$P=\frac{4}{10}=\frac{2}{5}$