Solution

The correct answer is Option 2) 3/5

Key Points

• Total numbers in the set = 200 (all integers from 1 to 200 inclusive).
• We want numbers divisible by 2 or 5. Use inclusion–exclusion.
• Multiples of 2 up to 200 = ⌊200/2⌋ = 100.
• Multiples of 5 up to 200 = ⌊200/5⌋ = 40.
• Numbers counted twice (multiples of both 2 and 5 = multiples of 10) = ⌊200/10⌋ = 20.
• Favourable count = 100 + 40 − 20 = 120.

Probability = favourable / total = 120 / 200 = 12/20 = 3/5.

Quick Check (Complement Method)

• Numbers not divisible by 2 or 5 end with digits {1,3,7,9} → 4 out of every 10 numbers.
• Count = (4/10) × 200 = 80. So probability of “not divisible by 2 or 5” = 80/200 = 2/5.
• Therefore, probability of “divisible by 2 or 5” = 1 − 2/5 = 3/5 (same result).