Question

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

Answer 1

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

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:

$P1 = \frac{7 girls}{9 students}$

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

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

$P2 = \frac{6 girls}{ 8 students}$

Then, the probability of the third girl:

$P3 = \frac{5 girls}{7 students}$

The fourth girl probability:

$P4 = \frac{4 girls}{ 6 students}$

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):

$P = P1*P2*P3*P4\\P = \frac{5}{18} \\P = 0.28 (or 28per cent)$

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