Question

A number is chosen at random from the list $\{2,3,5,7,11,13,17,19\}$. What is the probability of not choosing a prime number?

• A. 0
• B. $\frac{3}{8}$
• C. $\frac{5}{8}$
• D. $1$

Answer 1

The correct option is A 0

A number is chosen at random from the list $\{2,3,5,7,11,13,17,19\}$.

$\therefore$ Total number of possible outcomes= Number of numbers in the list= $8$

Prime numbers in the list= $\{2,3,5,7,11,13,17,19\}$, i.e., all numbers in the given list are prime numbers

$\therefore$ Number of favorable outcomes for choosing a prime number= Number of prime numbers in the list= $8$

Hence,
$\text{P(choosing a prime number)}=\frac{\text{Number of prime numbers in the list}}{\text{Total number of numbers in the list}}$

$\Rightarrow \text{P(choosing a prime number)}=\frac{8}{8}=1$

Now,

$\text{P(NOT choosing a prime number) = 1 - P(choosing a prime number)}$

$\Rightarrow \text{P(NOT choosing a prime number)}=1-1$

$\Rightarrow \text{P(NOT choosing a prime number)}=0$

$\therefore$ The probability of not choosing a prime number from the given list is $0$, i.e., from a list of all prime numbers, it is impossible NOT to choose a prime number.

Hence, an event of NOT choosing a prime number from a list of all prime numbers is an $\text{impossible event}$.