Question

The drawer in my house contains $6$ red handgloves and $14$ blue handgloves. If I randomly pick two handgloves, what is the probability that I'll have a pair of red handgloves?

• A. $\frac{3}{38}$
  
• B. $\frac{3}{10}$
  
• C. $\frac{5}{19}$
  
• D. $\frac{3}{39}$
  

Answer 1

The correct option is A $\frac{3}{38}$


Given:
$\bullet$ Total number of handgloves $=6+14=20$
$\bullet$ Number of red handgloves $=6$

First handglove:
The probability $\text{P(R1)}$ that the first handglove picked up is red is:

Number of red handgloves $=6$
Total number of handgloves $=6+14=20$

$\text{P(R1)}=\frac{\text{Number of red handgloves}}{\text{Total number of handgloves}}$

$\text{P(R1)}=\frac{6}{20}$

$\text{P(R1)}=\frac{3}{10}$


Second handglove:
Now, since the handglove picked up is not replaced by some other handglove.

Number of red handgloves available $=6-1=5$
Total number of handgloves available $=20-1=19$

The probability $\text{P(R2)}$ that the second handglove picked up is also red is:


$\text{P(R2)}=\frac{\text{Number of red handgloves}}{\text{Total number of handgloves}}$

$\text{P(R2)}=\frac{5}{19}$


The probability $\text{P(R1 and R2)}$ that the first handglove and the second handglove picked up is red would be obtained by multiplying $\text{P(R1)}$ and $\text{P(R2)}$.

$\text{P(R1 and R2)}=\text{P(R1)}\times \text{P(R2)}$

$\text{P(R1 and R2)}=\frac{3}{10}\times \frac{5}{19}$

$\text{P(R1 and R2)}=\frac{3}{38}$


The probability $\text{P(R1 and R2)}$ that the first handglove and the second handglove picked up is red is $\frac{3}{38}$.


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