The following two-way contingency table gives the breakdown of the population in

Question

The following two-way contingency table gives the breakdown of the population in a particular locale according to party affiliation (A, B, C, or None) and opinion on a bond issue:

A person is selected at random. Find the probability of each of the following events.

The person is affiliated with party B.

The person is affiliated with some party.

The person is in favor of the bond issue.

The person has no party affiliation and is undecided about the bond issue.

The person has no party affiliation or is in favor of the bond issue.

Affiliation Option Favors Opposes Undecided A 0.12 0.09 0.07 B 0.16 0.12 0.14 C 0.04 0.03 0.06 None 0.08 0.06 0.03

Explanation / Answer

1)

P(person is affiliated with party B) = 0.16 + 0.12 + 0.14 = 0.42

2)

P(person is affiliated with some party)

=P(person is affiliated with party A ) +P(person is affiliated with party B) + P(person is affiliated with party C)

= (0.12 + 0.09 + 0.07) + (0.16 + 0.12 + 0.14) + ( 0.04 + 0.03 + 0.06) = 0.28 + 0.42 + 0.13

= 0.83

3)

P(person is in the favour of the bond issue) = 0.12 + 0.16 + 0.04 + 0.08 = 0.40

4)

P( person has no party affiliation and is undecided about the bond issue ) = 0.03 (which is the value corresponding to the 4th row and 3rd column)

5)

P( person has no party affiliation or is in favor of the bond issue ) =

P( person has no party affiliation) + P( person is in favor of the bond issue) - P(person has no party affiliation and is in favor of the bond issue) =

(0.08 + 0.06+0.03) + (0.12 + 0.16 + 0.04 + 0.08) - 0.08 =

0.49

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