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Chapter 2: Q7E (page 57)

An academic department has just completed voting by secret ballot for a department head. The ballot box contains four slips with votes for candidate Aand three slips with votes for candidate B.Suppose these slips are removed from the box one by one.

a. List all possible outcomes.

b. Suppose a running tally is kept as slips are removed. For what outcomes does Aremain ahead of B throughout the tally?

Short Answer

Expert verified

a. The possible outcomes are,

\(S = \left\{ \begin{aligned}{l}BBBAAAA,BBABAAA,BBAABAA,BBAAABA,BBAAAB,BABBAAA,BABABAA,BABAABA,BABAAAB,\\BAABBAA,BAABABA,BAABAAB,BAAABBA,BAAABAB,BAAAABB,ABBBAAA,ABBABAA,ABBAABA,\\ABBAAAB,ABABBAA,ABABABA,ABABAAB,ABAABBA,ABAABAB,ABAABB,AABBBAA,AABBABA,\\AABBAAB,AABABBA,AABABAB,AABAABB,AAABBBA,AAABBAB,AAABABB,AAAABBB\end{aligned} \right\}\)

b. The possible outcomes are,

\(C = \left\{ {AABABAB,AABAABB,AAABBAB,AAABABB,AAAABBB} \right\}\)

Step by step solution

01

Given information

The number of slips the ballot box contains with votes for candidate A is 4.

The number of slips the ballot box contains with votes for candidate B is 3.

Theslips are removed from the box one by one.

02

List the possible outcomes in event S

a.

Let S represents the event of all possible outcomes.

The outcomes are represented as,

\(S = \left\{ \begin{aligned}BBBAAAA,BBABAAA,BBAABAA,BBAAABA,BBAAAB,BABBAAA,BABABAA,BABAABA,BABAAAB,\\BAABBAA,BAABABA,BAABAAB,BAAABBA,BAAABAB,BAAAABB,ABBBAAA,ABBABAA,ABBAABA,\\ABBAAAB,ABABBAA,ABABABA,ABABAAB,ABAABBA,ABAABAB,ABAABB,AABBBAA,AABBABA,\\AABBAAB,AABABBA,AABABAB,AABAABB,AAABBBA,AAABBAB,AAABABB,AAAABBB\end{aligned} \right\}\)

03

List of the possible outcomes

b.

A running tally is kept as slips are removed.

Let C be the event that A remains ahead of B throughout the tally.

The possible outcomes are,

\(C = \left\{ {AABABAB,AABAABB,AAABBAB,AAABABB,AAAABBB} \right\}\)

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