Question:
A number is selected at random from the numbers 1 to 30. What is the probability that the selected number is a prime number?
(a) $\frac{2}{3}$
(b) $\frac{1}{6}$
(C) $\frac{1}{3}$
(d) $\frac{11}{30}$
Solution:
Total number of outcomes = 30.
Prime numbers in 1 to 30 are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29.
Number of favourable outcomes = 10.
$\therefore \mathrm{P}$ (getting a prime number) $=\frac{\text { Number of favourable outcomes }}{\text { Number of all possible outcomes }}$
$=\frac{10}{30}=\frac{1}{3}$
Thus, the probability that the selected number is a prime number is $\frac{1}{3}$.
Hence, the correct answer is option (c).