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 allwinning coalitionsand identify thecritical membersin 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

Please give me a thumbs-up if this helps you out. Thank you!
**:)**

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