Question

Of the twenty-two students in a classroom, ten are transfer students, seven are nursing students, four are AAS students and one student is undecided.If three students are chose randomly, without replacement, find the probability that all three students are nursing students.

Answer 1

Given that:

• There are a total number of 22 students in the classroom.

,

• 10 of them are transfer students.

,

• 7 are nursing students.

,

• 4 are AAS students.

,

• 1 student is undecided.

,

• Three students are chosen randomly.

Since you need to find the probability that all three students that are chosen randomly are nursing students, you need to set up that this is:

`P(A)`

Where Event A is that one of the students is a nursing student.

Therefore, the probability that three of the chosen students are nursing students can be set up as:

`\begin{gathered} P=P(A)\cdot P(A)\cdot P(A)=P(A)^3 \\ \\ P=P(A)^3 \end{gathered}`

Knowing that the total number of students is 22 and 7 of them are nursing students, you know that:

`P(A)=(7)/(22)`

Therefore:

`P=((7)/(22))^3`
`P=0.0322`

Hence, the answer is:

`P=0.0322`