A political committee consists of seven Democrata and five Republicans. A subcom
ID: 3056643 • Letter: A
Question
A political committee consists of seven Democrata and five Republicans. A subcommittee of six people need to be formed from this group. Determine the probability that this subcommittee will consist of the following:
a. Two democrats and four Republicans if they were randomly selected.
b. Four Democrat and two Republicans if they were randomly selected,
C. Three Democrat and three Republicans if they were randomly selected.
d. Calculate the mean and standard deviation for the distribution which defines selecting a Republican as a success
e. Verify these results with excel.
Explanation / Answer
7 D + 5 R
Subcommittee of 6 needs to be selected
a) 2 D and 4 R
= [C(7,2)*C(5,4)]/C(12,6)
= [21*5]/924
= 0.113
b) 4 D and 2 R
= [C(7,4)*C(5,2)]/C(12,6)
= [35*10]/924
= 0.378
c) 3 D and 3 R
= [C(7,3)*C(5,3)]/C(12,6)
= [35*10]/924
= 0.378
d)
n = 6
p = 0.417
q = 0.583
Expected value= n*p = 6*0.417 = 2.502
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