Question

Alex has 12 blue shirts and 12 white shirts. Everyday he picks one shirt at random for office. After he has used that shirt, he chooses another shirt at random and wears them.What is the probability that he first picks a white shirt then a blue?

• A. $\frac{1}{4}$
• B. $\frac{2}{23}$
• C. $\frac{6}{23}$
• D. $\frac{1}{6}$

Answer 1

The correct option is C $\frac{6}{23}$

Given,
Alex has $12$ Blue and White shirts each.

Let $\text{A}$ and $\text{B}$ be two events of picking Blue and White shirt respectively.

Also, it is given that he does not replace the used shirt.

Probability of choosing White shirt first is $\text{P(B)}=\frac{12}{24}=\frac{1}{2}$

Probability of choosing Blue shirt after White shirt is chosen is $\text{P(A)}=\frac{12}{23}$

So, We have to calculate the probability that he first picks a white shirt then a blue shirt which is equal to $\text{P(E)}.$

$\Rightarrow \text{P(E)}=\text{P(B)}\times \text{P(A)}$

$\Rightarrow \text{P(E)}=\frac{1}{2}\times \frac{12}{23}=\frac{6}{23}$