A committee is to consist of a
Rubi Romo
Answered question
2022-04-29
A committee is to consist of a chair, three hagglers, and four do-nothings. The committee is formed by choosing randomly from a pool of 10 people and assigning them to the various "jobs."
(a) How many different committees are possible?
(b) Norman is eager to be the chair of the committee. What is the probability that he will get his wish? (Round your answer to two decimal places.)
(c) Norman's girlfriend Norma is less ambitious and would be happy to hold any position on the committee provided that Norman is also selected as a committee member. What is the probability that she will get her wish and serve on the committee? (Round your answer to two decimal places.)
(d) Norma does not get along with Oona (who is also in the pool of prospective members) and would be most unhappy if Oona were to chair the committee. Find the probability that all Norma's wishes will be fulfilled: She and Norman are on the committee, and it is not chaired by Oona. (Round your answer to two decimal places.)
Answer & Explanation
karton
Expert2022-07-07Added 613 answers
a. Sample space S consists of all possible committees. Let's find the cardinality of S using the following decision algorithm:
Step 1. Choose the chair. There are C(10,1) possibilities.
Step 2. Choose 3 hagglers. There are C(9,3) possibilities.
Step 3. Choose 4 do-nothings. There are C(6,4) possibilities.
The total number of committees is
b. Let E be the set of all committees in which Norman is the chair. Let's find the cardinality of
using the following decision algorithm:
Step 1. Choose the chair. There is only 1 possibility (Norman).
Step 2. Choose 3 hagglers. There are C(9,3) possibilities.
Step 3. Choose 4 do-nothings. There are C(6,4) possibilities.
Thus
The probability of Norman getting the chair is
c. Note that in this part, it does not matter who does what in the committee. There are in total committees of 8 people chosen from 10.
Out of those 45, there are committees that contain both Norman and Norma.
Therefore, the probability of Norma getting her wish and serving on the committee is
So,
(a) 12,600
(b) 1/10
(c) 28/45
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