Question

There are 32 students in Mrs. Worrell's Classroom. There 12 boys and 20 girls. She needs to select two students to represent her class for a Agora Student Math Department meeting. She will put all students names on a piece of paper and randomly select two names, one after the other. What is the probability that she will select a boy first and then a girl?

Answer 1

Answer:

15/64 = 23.4 %

Step-by-step explanation:

Let's consider the first two selections. Let's call B the case in which she extracts a boy and G the case in whish she extracts a girl.

For each selection, the probabilty of event B (selecting a boy) is

$P(B)=\frac{12}{32}=\frac{3}{8}$

While the probability of event G (selecting a girl) is

$P(G)=\frac{20}{32}=\frac{5}{8}$

We are asked to find the probability that the first two events are B and then G:

$P(B,G)$

In the first two selections, we have 4 possible combinations:

BB, BG, GB, GG

The probability for each combination is given by:

$P(BB)=P(B)\cdot P(B) = \frac{3}{8}\cdot \frac{3}{8}=\frac{9}{64}=14.1 \%$

$P(BG)=P(B)\cdot P(G) = \frac{3}{8}\cdot \frac{5}{8}=\frac{15}{64}=23.4 \%$

$P(GB)=P(G)\cdot P(B) = \frac{5}{8}\cdot \frac{3}{8}=\frac{15}{64}=23.4 \%$

$P(GG)=P(G)\cdot P(G) = \frac{5}{8}\cdot \frac{5}{8}=\frac{25}{64}=39.1 \%$

The second one is the probability we are searching for, so the probability that she will select a boy first and then a girl is 15/64, or 23.4%.