Question

the two - way relative frequency table shows the results of a survey on the mayors job approval. suppose a surveyor randomly selects a member of the sample population. use the table of relative frequencies to calculate each probability. express each probability as a decimal.
party affiliation

	republican	democrat	independent	total
	disapprove	0.22	0.1	0.12	0.44
	no opinion	0.03	0.07	0.04	0.14
total	0.39	0.42	0.19	1

sample problem
p(approve)
i can look at the value in the total column and approve row to determine p(approve).
0.42
p(independent or disapprove)

enter the answer in the space provided. use numbers instead of words.

Explanation:

Step1: Use the addition - rule of probability

The addition - rule for two events \(A\) and \(B\) is \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\). Let \(A\) be the event of being an Independent and \(B\) be the event of disapproving.

Step2: Identify individual probabilities

We know that \(P(\text{Independent}) = 0.19\), \(P(\text{disapprove})=0.44\), and \(P(\text{Independent and disapprove}) = 0.12\).

Step3: Calculate the probability

\[P(\text{Independent or disapprove})=P(\text{Independent})+P(\text{disapprove})-P(\text{Independent and disapprove})\]
\[P(\text{Independent or disapprove})=0.19 + 0.44- 0.12\]
\[P(\text{Independent or disapprove})=0.51\]

Answer:

0.51