Question

The Editor-in-Chief of the student newspaper was doing a final review of the articles submitted for the upcoming edition. Of the 12 total articles submitted, 5 were editorials. If he liked all the articles equally, and randomly selected 5 articles to go on the front cover, what is the probability that exactly 3 of the chosen articles are editorials? Write your answer as a decimal rounded to four decimal places.

Answer 1

This is a problem of binomial probability. We have two possible outcomes:

• the article selected is an editorial,

,

• the article selected is not an editorial.

The probability of success (select an article that is an editorial) is:

`p=(5)/(12)`

Because we have 12 total articles submitted, and 5 of them were editorials.

To calculate the probability that selecting 5 random articles, getting as a result that exactly 3 of the chosen articles are editorials, we use the binomial probability formula:

`P(n,x)=C(n,x)\cdot p^x\cdot(1-p)^(n-x)`

Where:

• n = the number of trials = the number of articles selected randomly = 5,

,

• x = the number of success = the number of editorials that we expect = 3,

,

• p = the probability of getting an editorial = 5/12,

,

• C(n,x) = n! / (x! (n-x)!).

Replacing the data in the formula above, we get:

`P(n=5,x=3)=(5!)/(3!\cdot(5-3)!)\cdot((5)/(12))^3\cdot(1-(5)/(12))^(5-3)\cong0.24615=0.2462`

Answer

Rounded to four decimal places, the probability that exactly 3 of the chosen articles are editorials is 0.2462.