Question

A class consists of 12 boys and 12 girls. The teacher picks five students to present their work to the rest of the class

and says that the five students are being selected at random. The students chosen are all girls.
a. If the teacher was truly selecting the students at random, what would the probability be that all five students
selected are girls? (Round your answer to the nearest thousandth.)
b. Does the fact that all five students selected are girls lead you to suspect that the teacher was not truly
selecting the students at random but that the teacher had a preference for choosing girls? Explain your
answer using the probability in part (a). \

Answer 1

0.01863, yes preference

Explanation:

given that a class consists of 12 boys and 12 girls. The teacher picks five students to present their work to the rest of the class and says that the five students are being selected at random

Here selecting any 5 students from the group of total 24 students is combination because order does not matter.

Total no of ways of selecting any 5 from total 24 =
`24C5\\=42504`

No of ways of selecting only 5 girls = No of ways of selecting random 5 girls from total 12 girls

=
`12C5\\=792`

a) the probability be that all five students

selected are girls=
`(792)/(42504) \\=0.01863`

b) Since the probability for selecting all girls is very small and near to 0, it is unusual to select all girls if done at random. Hence the teacher had a preference for girls.