Question

There are 9 students in a class: 2 boys and 7 girls. If the teacher picks a group of 4 at random, what is the probability that everyone in the group is a girl?

Answer 1

Answer:

28% probability that every student in the group is a girl.

Step-by-step explanation:

In this problem we have independent events, that is, the event "picking a girl" doesn't affect an "picking a boy", also, picking picking a girl doesn't affect the probability of the other subjects.

So, the probability when the first girl is being picked is:

$P_{1}=\frac{7 \ girls}{9 \ students}$

Because among the total 9 students, there are 7 girls.

Now, after picking one girl, there remains 6 girls and 8 students to be picked. So, the probability of the second girl would be:

$P_{2}=\frac{6 \ girls}{8 \ students}$

Then, the probability of the third girl:

$P_{3}=\frac{5 \ girls}{7 \ students}$

The fourth girl probability:

$P_{3}=\frac{4 \ girls}{6 \ students}$

Therefore, the probability of picking all 4 girls would be the product of each probability, because events are independent (we use product when they are independent):

$P=\frac{7 \ girls}{9 \ students} \times \frac{6 \ girls}{8 \ students} \times \frac{5 \ girls}{7 \ students} \times \frac{4 \ girls}{6 \ students}\\P=\frac{5}{18}=0.28 \ (or \ 28\%)$

Therefore, there's 28% probability that every student in the group is a girl.