Question

A committee is selected to vote yes or no on a proposed location for a new parts distribution
center. The committee is composed of

 three people who live in (A)bbeytown, 

five people who live in (B)arnsborough, 

six people who live in (C)hatterville, and 

eight people who live in (D)itherburgh. 

At least 17 votes are required for a decision, and the committee members will
vote in blocs according to their places of residence. List all winning coalitions and identify
the critical members in these coalitions.

Problem 2 (2016Fall)

For a school project, Sue interviewed a total of 100 persons who were either lawyers or sales-
men. She asked them if they were happy or unhappy with their occupation. Of the 61 lawyers
interviewed, 15 were unhappy, however, only 4 of the salesmen were unhappy. Suppose that
one of the persons interviewed is selected at random.
(a) Find the probability that the person selected is a salesman.
(b) Find the probability that the person selected is happy.
(c) If we know that the selected person is a lawyer, what is the probability that the person
is happy.

Answer 1

Problem 2

(a) Find the probability that the person selected is a salesman.

= 1-61/100 = 0.39
(b) Find the probability that the person selected is happy.

A - event hat person is happy

L - lawyer

S- Salesman

P(A) = P(A| L)P(L) + P(A|S) P(S)

= (61-15)/61 * 61/100 + (39-4)/39*39/100

= 1-(15 + 4)/100

= 1-19/100

=0.81
(c) If we know that the selected person is a lawyer, what is the probability that the person
is happy.

P(A|L) = P(A and L)/P(L)

= (61-15)/100 / 0.61

= 0.75409

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