A number is selected at random from the numbers 1 to 30. The probability that it is a prime number:
$( A) \ \frac{2}{3}$
$( B) \ \frac{1}{6}$
$( C) \ \frac{1}{3}$
$( D) \ \frac{11}{30}$

Academic Mathematics NCERT Class 10

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

To do: To find the probability that it is a prime number.

Solution: Total number of possible outcomes $=30$

Prime numbers between 1 to 30 are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29

Total number of favourable outcomes $=\ 10$

Probability of selecting a prime number from 1 to 30$=\frac{Total\ number\ of\ favourable\ outcomes}{Total\ number\ of\ outcomes}$

$=\frac{10}{30}$

$=\frac{1}{3}$

Hence, The correct option is $( C)$

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Updated on: 10-Oct-2022

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