Question

Suppose a number is chosen at random from $1$ to $20$. What is the probability that the chosen number is a prime number?

• A. $\frac{{}^9{C}_1}{{}^{20}{C}_1}$
  
• B. $\frac{{}^8{C}_1}{{}^{20}{C}_1}$
  
• C. $\frac{{}^8{C}_1}{{}^9{C}_1}$
  
• D. $\frac{{}^9{C}_1}{{}^{19}{C}_1}$
  

Answer 1

The correct option is B $\frac{{}^8{C}_1}{{}^{20}{C}_1}$


Prime numbers between $1$ to $20$ are:
$2,3,5,7,11,13,17,19$ ($\because 1$ is neither prime nor composite)

Total prime numbers between $1$ to $20$ are $8$.
Let $\text{P(Prime)}$ denotes the probability of selecting a prime number from $1$ to $20$.

Number of favorable outcomes $=$ Selecting a prime number from $8$ prime numbers $={}^8{C}_1$
Total number of outcomes $=$ Selecting a number from $1$ to $20={}^{20}{C}_1$

$\text{P(Prime)}=\frac{\text{Selecting a prime number from 8 prime numbers}}{\text{Selecting a number from 1 to 20}}$

$\text{P(Prime)}=\frac{{}^8{C}_1}{{}^{20}{C}_1}$

Therefore, option (b.) is the correct answer.