Question

Two students from a group of eight boys and 12 girls are sent to represent the school in a parade if the students are chosen at random what is the probability that the student is chosen or not both girls

Answer 1

62/95,

Explanation:

Answer 2

62/95, or 0.6526

Explanation:

To solve this, we fill find the probability that both students chosen are girls. We will then find the complement of this, which will be that not both students are girls.

First we find the number of ways we can choose 0 boys from a group of 8. This is the combination

`_8C_0=(8!)/((8-0)!0!)=(8!)/(8!0!)=1`

Next we find the number of ways we can choose 2 girls from a group of 12. This is the combination

`_(12)C_2=(12!)/((12-2)!2!)=(12!)/(10!2!)=(12(11))/(2(1))=66`

This gives us 1*66 = 66 ways the event "both students are girls" can happen.

Next we find the total number of ways to choose 2 students out of this group. There are a total of 8+12 = 20 students; this is the combination

`_(20)C_2=(20!)/((20-2)!2!)=(20!)/(18!2!)=(20(19))/(2(1))=190`

This gives us the probability 66/190, which simplifies to 33/95.

We want the complement of this. That means we subtract this probability from 1:

1-33/95 = 62/95 = 0.6526