Question

12) A study conducted at a certain college shows that 55% of the school's graduates find a job in their chosen field within a year after graduation. Find the probability that among 7 randomly selected graduates, at least one finds a job in his or her chosen field within a year of graduating

Answer 1

`P(At\ least\ 1) = 0.9963`

Explanation:

Represent the probability that a graduate finds a job with p

`p = 55\%`

Required

Determine the probability that at least 1 of 7 gets a job.

In probability:

`P(At\ least\ 1) = 1 - P(None)`

So, we calculate the probability that none of the 7 gets a job.

Represent the probability that a graduate will not get a job with q.

`q= 1 - p`

`q= 1 - 55\%`

`q=45\%`

Represent as decimal

`q = 0.45`

The probability that none of the 7 will get a job is
`q^7`

i.e.

`P(None) = q^7`

So, we have:

`P(At\ least\ 1) = 1 - P(None)`

`P(At\ least\ 1) = 1 - q^7`

Substitute 0.45 for q

`P(At\ least\ 1) = 1 - 0.45^7`

`P(At\ least\ 1) = 1 -0.00373669453`

`P(At\ least\ 1) = 0.99626330547`

`P(At\ least\ 1) = 0.9963` -- approximated