Question

A jury pool has 15 people that are married and 20 people that are not married, 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 probability that the jury consists of the following. (Give answer as a fraction or a decimal out to at least 4 places. If your answer is very small use scientific notation out to 4 decimal places for example 3.3421E-6.)

Answer 1

a

`P(K) = 0`

b

`P(Z) = 0`

c

`P(W) = 0.1016`

d

`P(R) = 0.29`

Explanation:

From the question we are told that

The number of married people is k = 15

The number of people that are not married is u = 15

The number of people selected is e = 12

The total number of people is n = 30

Generally the number of ways of selecting 12 people from the married people is mathematically represented as

`B = ^k C_e`

Here C stands for combination hence we will be making use of the combination functionality in our calculators

`B = ^(15) C_(12)`

=>
`B = 455`

Generally the number of ways of selecting 0 people from the not married people is mathematically represented as

`A = ^u C_0`

=>
`A = ^(15) C_0`

=>
`A = 1`

Generally the number of ways of selecting 12 people from the total number of people is mathematically represented as

`D = ^(n) C_(12)`

=>
`D = ^(30) C_(12)`

=>
`D = 8.6493225 *10^(7)`

Generally the number of ways of selecting 12 people from the married people is equal to the number of ways of selecting 12 people from not married, also the number of ways of selecting 0 people from the not married is equal to the number of ways of selecting 0 people from the married people, all this is because the number of married people is equal to the number of not married people

Generally the number of ways of selecting 8 people from the married people is

`E = ^(k) C_(8)`

=>
`E = ^(15) C_(8)`

=>
`E =6435`

Generally the number of ways of selecting 4 people from the not married people is

`F = ^(u) C_(4)`

=>
`F= ^(15) C_(4)`

=>
`F=1365`

Generally the number of ways of selecting 6 people from the married people is

`G = ^(k) C_{6`

=>
`G= ^(15) C_(6)`

=>
`G=5005`

Generally the number of ways of electing 6 people from the married people is equal to the number of ways of selecting 6 people from the not married people

Generally the probability that the jury consists of all married people is mathematically represented as

`P(K) = (455 * 1 )/(8.6493225 *10^(7))`

=>
`P(K) = (455 * 1 )/(8.6493225 *10^(7))`

=>
`P(K) = 0.000005`

=>
`P(K) = 0`

Generally the probability that the jury consists of all not married people is mathematically represented as

`P(Z) = (455 * 1 )/(8.6493225 *10^(7))`

=>
`P(Z) = (455 * 1 )/(8.6493225 *10^(7))`

=>
`P(Z) = 0.000005`

=>
`P(Z) = 0`

Generally the probability that the jury consists of 8 married and 4 that are not married is mathematically represented as

`P(W) = ( E * F)/(D)`

=>
`P(W) = ( 6435 * 1365)/(8.6493225 *10^(7))`

=>
`P(W) = 0.1016`

Generally the probability that the jury consists of 6 married and 6 that are not married. is mathematically represented as

`P(R) = (G * G)/(D)`

`P(R) = (5005 * 5005)/(8.6493225 *10^(7))`

=>
`P(R) = 0.29`