Eighty cards are numbered from 1 to 80, one number on each card. One card is drawn at random. What is the probability that the number on the card is a multiple of both 4 and 6?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(\frac{3}{40}\)
A number is a multiple of both 4 and 6 when it is a multiple of their LCM, 12 (not of their product 24). The 80 cards are equally likely, so the probability is the number of such cards divided by 80.
LCM of 4 and 6 \(=12\)
Multiples of 12 from 1 to 80: 12, 24, 36, 48, 60, 72, that is 6 cards
Probability \(\displaystyle =\frac{6}{80}=\frac{3}{40}\)