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 five students are chose randomly, with replacement, find the probability that at least one student is a transfer student.

Answer 1

Given that,

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 five students are chose randomly, with replacement, To find the probability that at least one student is a transfer student.

Total number of students=22

To select 5 students, we get,

Total possible outcomes is,

`22^5`

First we find the probability of selecting 5 students with replacement not in transfer students,

we get,

Number of required outcomes is,

`12^5`

Probability of selecting 5 students none of them are transfered students is

`=(12^5)/(22^5)`
`=((12)/(22))^5`
`=((6)/(11))^5=0.04828`

the probability that at least one student is a transfer student is,

`=1-0.04828`
`=0.9517`

Answer is: 0.9517