Respuesta :
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:
[tex]p=\frac{5}{12}[/tex]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:
[tex]P(n,x)=C(n,x)\cdot p^x\cdot(1-p)^{n-x}[/tex]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:
[tex]P(n=5,x=3)=\frac{5!}{3!\cdot(5-3)!}\cdot(\frac{5}{12})^3\cdot(1-\frac{5}{12})^{5-3}\cong0.24615=0.2462[/tex]Answer
Rounded to four decimal places, the probability that exactly 3 of the chosen articles are editorials is 0.2462.
