A number is chosen at random from 40 and 50 inclusive. Find the probability that the number is prime.

Analyze the question: We choose a number from 40 to 50 inclusive. We need the probability that it is prime.

Concept: Probability = (number of favourable outcomes) ÷ (total number of outcomes). A prime number has exactly two factors: 1 and itself.

Step 1: Total outcomes The numbers are 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50. Total = 50 − 40 + 1 = 11

Step 2: Identify the primes

• 40: even, not prime
• 41: not divisible by 2, 3, 5 (and 7² = 49 > 41), so prime
• 42: even
• 43: not divisible by 2, 3, 5, so prime
• 44: even
• 45: divisible by 5
• 46: even
• 47: not divisible by 2, 3, 5, so prime
• 48: even
• 49: 7 × 7, not prime
• 50: even

Primes: 41, 43, 47, which gives 3 primes.

Step 3: Probability P(prime) = 3/11

Tip: To test primality of numbers below 100, you only need to check divisibility by 2, 3, 5 and 7. Also, remember to count inclusively: the number of integers from a to b is b − a + 1. Many students lose marks by forgetting the "+1".