A jury pool consists of 31 people, 13 men and 18 women. Compute the probability that a randomly selected jury of 12 people is all male.

Respuesta :

The first person you select has a probability of

[tex]\frac{13}{31}[/tex]

of being a male. The second time, there is a probability of:

[tex]\frac{12}{30}\text{.}[/tex]

Following the same reasoning, the probability of selecting 12 males is:

[tex]\frac{13}{31}\cdot\frac{12}{30}\cdot\frac{11}{29}\cdot\frac{10}{28}\cdot\frac{9}{27}\cdot\frac{8}{26}\cdot\frac{7}{25}\cdot\frac{6}{24}\cdot\frac{5}{23}\cdot\frac{4}{22}\cdot\frac{3}{21}\cdot\frac{2}{20}\text{.}[/tex]

Simplifying the above multiplication, we get:

[tex]\frac{13!}{31\cdot30\cdot29\cdot28\cdot27\cdot26\cdot25\cdot24\cdot23\cdot22\cdot21\cdot20}\approx9.2\times10^{-8}\text{.}[/tex]

Answer:

[tex]9.2\times10^{-8}=0.000000092.[/tex]