Question

www.g "7 Democrats and 6 Republicans. Four members are selected to attend a conference. Find the probability that the group will consist of all Republicans."

Answer 1

2.10% probability that the group will consist of all Republicans.

Explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

In this question, the order in which the members are selected is not important. So we use the combinations formula to solve this question.

Combinations formula:

`C_(n,x)` is the number of different combinations of x objects from a set of n elements, given by the following formula.

`C_(n,x) = (n!)/(x!(n-x)!)`

Desired outcomes:

4 republicans from a set of 6.

`D = C_(6,4) = (6!)/(4!2!) = 15`

Total outcomes:

4 members from a set of 6 + 7 = 13.

`T = C_(13,4) = (13!)/(4!9!) = 715`

Probability:

`p = (D)/(T) = (15)/(715) = 0.021`

2.10% probability that the group will consist of all Republicans.