Question

A study conducted at a certain college shows that 58% 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

Solution;
Given: n =7
58% of the school's garduates find job in the their chosen field within a year after garduation.
p= 0.58
q=1-p= 0.42
The pmf of a random variable x is given as,
P(x)=nCx (p^x)[q^(n-x)]
=7Cx (0.58^x)[0.42^(7-x)]
P(at least one find job in his or her chosen field within a year after garduating.)=P(x>=1)
= 1- P( x<1)
= 1- P(x=0)
=1- 7C0 (0.58^0)[0.42^(7-0)]
=1- (1) (1)(0.42)
= 1- 0.0023
= 0 9977
Probability that at least one find job in his or her chosen field within a year after garduating is 0.9977