Fifty cards are numbered from 1 to 50, 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 3 and 4?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(\frac{2}{25}\)
A number is a multiple of both 3 and 4 when it is a multiple of their LCM, 12. The 50 cards are equally likely, so the probability is the number of such cards divided by 50.
LCM of 3 and 4 \(=12\)
Multiples of 12 from 1 to 50: 12, 24, 36, 48, that is 4 cards
Probability \(\displaystyle =\frac{4}{50}=\frac{2}{25}\)