Q.A fair die is rolled once. Find the probability of getting a number greater than 4.

Identify which die faces are greater than 4, then apply the classical probability formula.

The sample space for a single fair die roll is $S=\{1,2,3,4,5,6\}$, $n(S)=6$, with every outcome equally likely.

The event $E =$ 'getting a number greater than 4' includes the outcomes strictly greater than 4: $E = \{5, 6\}$, so $n(E) = 2$.

By the classical definition (§5): $P(E) = \dfrac{n(E)}{n(S)} = \dfrac{2}{6} = \dfrac{1}{3}$. …

Alternative — via the complement directly: $P(\text{number} \le 4) = \dfrac{4}{6}=\dfrac23$, so $P(\text{ …

A common error is including 4 itself in the favourable outcomes (misreading 'greater than 4' as 'greater than or equal to 4'), which would wrongly give $n(E)=3$ and $P(E)=\tfrac12 …