A die is thrown once. The probability of getting a number which is a prime number or a multiple of 3 is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(\displaystyle\frac{2}{3}\)
The sample space has 6 equally likely outcomes: 1, 2, 3, 4, 5, 6.
Prime numbers: 2, 3, 5
Multiples of 3: 3, 6
The number 3 is in both lists, so it is counted only once. The favourable outcomes are 2, 3, 5, 6.
\( \displaystyle P = \frac{4}{6} \)
\( \displaystyle = \frac{2}{3} \)
Why the other options are incorrect
Option (1) \(\displaystyle\frac{5}{6}\) — Incorrect. This is \(\frac{3}{6} + \frac{2}{6}\), which counts the number 3 twice.
Option (2) \(\displaystyle\frac{1}{2}\) — Incorrect. This is the probability of a prime number only (3 outcomes out of 6).
Option (4) \(\displaystyle\frac{1}{6}\) — Incorrect. This is the probability of getting 3, a number that is both prime and a multiple of 3.