Question

$150$ people line up to buy raffle tickets. Every tenth person who buys a ticket gets a pack of chocolates as a promotional item. What is the probability that a randomly chosen person from the line will receive a pack of chocolates?

• A. $\frac{1}{15}$
  
• B. $\frac{1}{10}$
  
• C. $\frac{1}{150}$
  
• D. $\frac{10}{15}$
  

Answer 1

The correct option is B $\frac{1}{10}$


There are $150$ people which means $15$ groups of $10$ persons each.

As per the question, every ${10}^{th}$ person is getting a pack of chocolates, $15$ persons would receive a pack of chocolates.

Let $\text{P(E)}$ denotes the probability that a person receives a pack of chocolates.

Number of favorable outcomes $=$ Selecting a person who receives a pack of chocolates $={}^{15}{C}_1$
Total number of outcomes $=$ Selecting a random person from $150$ persons $={}^{150}{C}_1$


$\text{P(E)}=\frac{\text{Selecting a person who receives a pack of chocolates}}{\text{Selecting a random person from 150 persons}}$
$\text{P(E)}=\frac{{}^{15}{C}_1}{{}^{150}{C}_1}$

$\text{P(E)}=\frac{15}{150}(\because {}^n{C}_1=\frac{n!}{1!(n-1)!}=n)$

$\text{P(E)}=\frac{1}{10}$

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