Assume that the committee consists of 8 republicans. and 5 democrats. a subcommittee of 4 is randomly selected from all subcommittees of 4 which contain at least 1 democrat. what is the probability that the new subcommittee will contain at least 2 democrats?

The probability that the new subcommittee will contain at least 2 Democrats is about 0.57.

Step-by-step explanation:

Given information:

Republicans = 8

Democrats = 5

Total committee = 13

Possible ways to select 0 Democrat in group of 4 subcommittees.

Possible ways to select 1 Democrat in group of 4 subcommittees.

Possible ways to select 2 Democrat in group of 4 subcommittees.

Possible ways to select 3 Democrat in group of 4 subcommittees.

Possible ways to select 4 Democrat in group of 4 subcommittees.

Total possible ways to select at least 1  Democrat in group of 4 subcommittees is

Total possible ways to select at least 2  Democrat in group of 4 subcommittees is

The formula for probability is

Therefore, the probability that the new subcommittee will contain at least 2 Democrats is about 0.57.