Question

An interviewer is given a list of potential people she can interview. She needs five interviews to complete her assignment. Suppose that each person agrees independently to be interviewed with probability 2/3. What is the probability she can complete her assignment if the list has______.

(a) 5 names?
(b) What if it has 8 names?
(c) If the list has 8 names what is the probability that the reviewer will contact exactly 7 people in completing her assignment?
(d) With 8 names, what is the probability that she will complete the assignment without contacting every name on the list?

Answer 1

Answer: a)
`(32)/(243)` b)
`(256)/(6561)` c)
`(128)/(6561)` d)
`(6305)/(6561)`

Explanation:

Since we have given that

Probability that each person agrees independently to be interviewed =
`(2)/(3)`

(a) 5 names?

If it has 5 names, then the probability would be

`((2)/(3))^5\\\\=(32)/(243)`

(b) What if it has 8 names?

If it has 8 names, then the probability would be

`((2)/(3))^8=(256)/(6561)`

(c) If the list has 8 names what is the probability that the reviewer will contact exactly 7 people in completing her assignment?

`^8C_7((2)/(3))^7((1)/(3))\\\\=(128)/(6561)`

(d) With 8 names, what is the probability that she will complete the assignment without contacting every name on the list?

`1-P(X=8)\\\\=1-^8C_8((2)/(3))^8\\\\=1-(256)/(6561)\\\\=(6561-256)/(6561)\\\\=(6305)/(6561)`

Hence, a)
`(32)/(243)` b)
`(256)/(6561)` c)
`(128)/(6561)` d)
`(6305)/(6561)`