Question

A number is drawn from first 30 natural numbers and it appears to be an odd number. Find the probability of the number so drawn being a prime number.

• A. $\frac{3}{5}$
• B. $\frac{5}{17}$
• C. $\frac{15}{33}$
• D. $\frac{14}{33}$

Answer 1

Answer: (A)

$\frac{3}{5}$

Total number are 30.

Odd numbers in first 30 natural numbers are $1,3,5,7,9,11,13,15,17,19,21,23,25,27,29$, $n\left(S\right)=15$

Out of these number of prime numbers are {3, 5, 7, 11, 13, 17, 19, 23, 29}, $n\left(E\right)=9$

Hence probability of the number so drawn being a prime number, $\frac{n\left(E\right)}{n\left(S\right)}=\frac{9}{15}=\frac{3}{5}$