If $x = 3^a + 3^{-a}$ is a positive integral value, then the probability that $x$ will have $3$ in its units place is
Step-by-Step Solution
Key Concept: Probability is the ratio of favorable outcomes to total possible outcomes for equally likely events.
Given that $n_x = 3n$, where $n$ is a positive integral value. Only four digits may be at the unit place: 1, 3, 7, 9. Let $E$ be the event of getting 4 at its unit place. Then $n(E) = 1$. Therefore, $P(E) = \frac{n(E)}{n(S)} = \frac{1}{4}$.
Correct Answer: 1