SOLUTION: A committee of two is selected at random from a set consisting of three Democrats, four Republicans and one Independent.
(a) What is the probability that the committee consists
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Question 279849: A committee of two is selected at random from a set consisting of three Democrats, four Republicans and one Independent.
(a) What is the probability that the committee consists of no Republicans?
(b) What is the probability that the committee consists of all Republicans?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
There are 4 ways out of 8 to select other than a Republican for the first position on the committee. Once the first position has been filled and it is known that it is not a Republican, then there remain 3 ways out of 7 to select other than a Republican, hence the Probability of no Republicans is:
\left(\frac{3}{7}\right)\ =\ \left(\frac{3}{14}\right))
The other part of this problem is left as an exercise for the student.
Super Double Plus Extra Credit: What is the probability of exactly 1 Republican? Remember, sometimes it is easier to find the probability of anything else happening and then subtract from 1.
John
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