A number is selected at random from the numbers 1 to 30.

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).

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