Question

A 2017 poll found that 51​% of college students were very confident that their major will lead to a good job. If 15 college students are chosen at​ random, what's the probability that 11 of them are NOT confident that their major would lead to a good​ job? Let a success be a college student not being confident their major would lead to a good job.

Answer 1

3.61%

Explanation:

This situation can be modeled with the Binomial Distribution which computes the likelihood of an event “success” that occurs exactly k times out of n, and is given by

`\large P(k;n)=\binom{n}{k}p^kq^(n-k)`

where

`\large \binom{n}{k}`= combination of n elements taken k at a time.

p = probability that the event (“success”) occurs once

q = 1-p

In this case, we define “success” as a college student not being confident that their major would lead to a good job.

Then

p = 49% = 0.49

q = 51% = 0.51

“If 15 college students are chosen at​ random, what's the probability that 11 of them are NOT confident that their major would lead to a good​ job?”

Here we are looking for P(11;15)

`\large P(11;15)=\binom{15}{11}0.49^(11)0.51^((15-11))=0.03611=3.61\%`