Answer: [tex]\dfrac{7}{1,337,220}=5.2\times 10^{-6}[/tex]
Step-by-step explanation:
Order does not matter so it is a Combination.
There are 14 men and we are going to choose 12 --> ₁₄C₁₂
There are 27 people and we are going to choose 12 --> ₂₇C₁₂
[tex]\dfrac{_{14}C_{12}}{_{27}C_{12}}\rightarrow\dfrac{14!}{(14-12)!}\div \dfrac{27!}{(27-12)!}=\large\boxed{\dfrac{7}{1,337,220}}[/tex]
Probabilities are used to determine the chances of an event
The probability of selecting 12 males is: [tex]\frac{7}{1337220}[/tex]
The parameters are given as:
[tex]n = 24[/tex] --- sample size
[tex]Male = 14[/tex]
[tex]Female = 13[/tex]
[tex]r = 12[/tex] ---- number of jury pool
The number of ways of selecting 12 members of the jury, from a total of 27 is:
[tex]^nC_r = \frac{n!}{(n - r)!r!}[/tex]
So, we have:
[tex]^{27}C_{12} = \frac{27!}{(27 - 12)!12!}[/tex]
[tex]^{27}C_{12} = \frac{27!}{15! \times 12!}[/tex]
[tex]^{27}C_{12} = 17383860[/tex]
The number of ways of selecting 12 members of the jury, from a total of 14 male is:
[tex]^nC_r = \frac{n!}{(n - r)!r!}[/tex]
So, we have:
[tex]^{14}C_{12} = \frac{14!}{(14 - 12)!12!}[/tex]
[tex]^{14}C_{12} = \frac{14!}{2! \times 12!}[/tex]
[tex]^{14}C_{12} = 91[/tex]
So, the probability of selecting 12 males is:
[tex]Pr = \frac{^{14}C_{12}}{^{27}C_{12}}[/tex]
[tex]Pr = \frac{91}{17383860}[/tex]
Simplify
[tex]Pr = \frac{91/13}{17383860/13}[/tex]
[tex]Pr = \frac{7}{1337220}[/tex]
Hence, the required probability is: [tex]\frac{7}{1337220}[/tex]
Read more about probabilities at:
https://brainly.com/question/11234923
