Question

Wardrobe of Samuel has $5$ pairs of socks, $7$ pairs of shoes and $10$ shirts. If Samuel picks an item at random, what is the probability that the picked item is a shirt? (Consider a pair of socks or shoes as one item)

• A. $\frac{10}{11}$
  
• B. $\frac{5}{11}$
  
• C. $\frac{6}{11}$
  
• D. $\frac{5}{22}$
  

Answer 1

The correct option is B $\frac{5}{11}$


Given:
$\bullet$ Number of pairs of socks $=5$
$\bullet$ Number of pairs of shoes $=7$
$\bullet$ Number of shirts $=10$

Total number of items available in Samuel's wardrobe $=$ Number of pairs of socks $+$ Number of pairs of shoes $+$ Number of shirts
$=5+7+10$
$=22$

Let $\text{P(Shirt)}$ denotes the probability that the picked item is a shirt.

Number of favorable outcomes $=$ Number of shirts $={}^{10}{C}_1$
Number of possible outcomes $=$ Total number of items available in Samuel's wardrobe $={}^{22}{C}_1$

$\text{P(Shirt)}=\frac{\text{Number of shirts}}{\text{Total number of items available in Samuel's wardrobe}}$

$\text{P(Shirt)}=\frac{{}^{10}{C}_1}{{}^{22}{C}_1}$

$\text{P(Shirt)}=\frac{10}{22}$

$\text{P(Shirt)}=\frac{5}{11}$

The probability that the picked item is a shirt is $\frac{5}{11}$.

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