Question

A jury pool has 17 men and 24 women, from which 12 jurors will be selected. Assuming that each person is equally likely to be chosen and that the jury is selected at random, find the following probabilities:

Give all answers accurate to six decimal places.

a) all men
b)all women
c) 8 men 4 women
d) 6 men 6 women

Answer 1

since
`17+24=41`

a)
`\frac{\binom{17}{12}}{\binom{42}{12}}`

b)
`\frac{\binom{24}{12}}{\binom{42}{12}}`

c)
`\frac{\binom{17}{8} \cdot \binom{24}{4}}{\binom{42}{8}\cdot\binom{36}{4}}`

d)
`\frac{\binom{17}{6}\cdot\binom{24}{6}}{\binom{17}{6}\cdot\binom{36}{6}}`

Just calculate these. If there is anything wrong just let me know.