Question

The Louisiana State Senate contains 14 Democrats and 25 Republicans. A committee of 4 members is being selected. Use this information to answer the following.

Step 1 of 5: If the committee is selected at random, what is the probability that all of the members are Democrats?

Step 2 of 5:

If the committee is selected at random, what is the probability that all of the members are Republicans?

Step 3 of 5:

If the committee is selected at random, what is the probability that 2 members are Democrats and the rest are Republicans?

Step 4 of 5:

Interpret your answer from the previous step.

Step 5 of 5:

Consider your answers from the first three steps. Were any of these events unusual? If so, list the step number(s) below. If not, write none.

Answer 1

Step 1 of 5: probability that all of the members are Democrats =(14C4)./(39C4)=1001/82251

=0.0122

Step 2 of 5: probability that all of the members are Republicans =(25C4)./(39C4)=12650/82251

=0.1538

Step 3 of 5: probability that 2 members are Democrats and the rest are Republicans

=(14C2)*(25C2)./(39C4)=91*300/82251= 0.3319

Step 4 of 5: if a large number of sample of size 4 is taken from above populaiton then almost 15.38 % will have 2 members as Democrats and the rest are Republicans

Step 5 of 5: Step1 (since its probability is less than 0.05)