Question

A bag contains $4$ red, $3$ green and $5$ blue balls. A ball is drawn at random, what is the probability that it is a blue ball?

• A. $\frac{{}^5{C}_1}{{}^{12}{C}_5}$
  
• B. $\frac{{}^5{C}_1}{{}^{12}{C}_1}$
  
• C. $\frac{1}{{}^{12}{C}_1}$
  
• D. $\frac{1}{{}^5{C}_1}$
  

Answer 1

The correct option is B $\frac{{}^5{C}_1}{{}^{12}{C}_1}$


Total number of balls available in the bag $=4+3+5=12$
Number of blue balls $=5$

Let $\text{P(B)}$ denotes the probabilty that the ball picked up is blue.

Number of favorable outcomes $=$ Selecting a blue ball from $5$ blue balls $={}^5{C}_1$
Total number of outcomes $=$ Selecting a ball from $12$ balls $={}^{12}{C}_1$

$\text{P(B)}=\frac{\text{Selecting a blue ball from 5 blue balls}}{\text{Selecting a ball from 12 balls}}$
$\text{P(B)}=\frac{{}^5{C}_1}{{}^{12}{C}_1}$

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