Question

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?

Answer 1

The probability that the new subcommittee will contain at least 2 Democrats is 365/ 645 or 0.5658914728682171. I am hoping that this answer has satisfied your query and it will be able to help you in your endeavor, and if you would like, feel free to ask another question.

Answer 2

Answer:

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.

$^8C_4\times ^5C_0=70\times 1=70$

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

$^8C_3\times ^5C_1=56\times 5=280$

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

$^8C_2\times ^5C_2=28\times 10=280$

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

$^8C_1\times ^5C_3=8\times 10=80$

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

$^8C_0\times ^5C_4=1\times 5=5$

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

$\text{Total outcomes}=280+280+80+5=645$

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

$\text{Favorable outcomes}=280+80+5=365$

The formula for probability is

$P=\frac{\text{Favorable outcomes}}{\text{Total outcomes}}$

$P=\frac{365}{645}$

$P=0.57$

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