A number is chosen at random from the whole numbers 1 to 60, both included. What is the probability that the number is divisible by 4 or by 10 (or by both)?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(\frac{3}{10}\)
Numbers divisible by both 4 and 10 are the multiples of their LCM, 20. They appear in both lists, so they are counted only once: n(A or B) = n(A) + n(B) − n(both).
Multiples of 4 from 1 to 60: \(60\div4=15\)
Multiples of 10 from 1 to 60: \(60\div10=6\)
Multiples of 20 from 1 to 60: \(60\div20=3\) (20, 40, 60)
Divisible by 4 or 10 \(=15+6-3=18\)
Probability \(\displaystyle =\frac{18}{60}=\frac{3}{10}\)