A die is tossed once. Find the probability of getting a prime number.

Analyze the question: A fair six-sided die has outcomes {1, 2, 3, 4, 5, 6}. We need the probability that the number showing is prime.

Concept: Probability = (number of favourable outcomes) ÷ (total number of possible outcomes).

A prime number is a number greater than 1 that has exactly two factors: 1 and itself. Note that 1 is not prime, and 2 is the only even prime.

Solution:

• Sample space: {1, 2, 3, 4, 5, 6}, so n(S) = 6
• Prime numbers in the sample space: • 1: not prime • 2: prime • 3: prime • 4: not prime (2 × 2) • 5: prime • 6: not prime (2 × 3)
• Favourable outcomes: {2, 3, 5}, so n(E) = 3

P(prime) = 3/6 = 1/2

Tip: For die questions, quickly list the primes: 2, 3, 5. Remember that 1 is never prime, since this is the most common trap in WASSCE and JAMB probability questions. Always simplify your fraction at the end (3/6 → 1/2).