Question

Teacher needs two students to help him with a science experiment for his class of 10 girls and 10 boys. He randomly picks two students one by one. What is the probability of choosing a boy then a girl?

• A. $\frac{10}{19}$
• B. $\frac{5}{19}$
• C. $\frac{1}{4}$
• D. $\frac{1}{10}$

Answer 1

The correct option is B $\frac{5}{19}$

Given there are $10$ boys and $10$ girls in class.

Let $\text{A}$ and $\text{B}$ be two events of picking boy and girl respectively.

Probability of choosing a boy is $\text{P(A)}=\frac{10}{20}=\frac{1}{2}$

Since replacement is not allowed, the probability of choosing a girl is $\text{P(B)}=\frac{10}{19}$

So, the probability of choosing a boy then a girl is $\text{P(E)}=\text{P(A)}\times \text{P(B)}$

$\Rightarrow \text{P(E)}=\frac{1}{2}\times \frac{10}{19}=\frac{5}{19}$