the two - way relative frequency table shows the results of a survey on the mayors job approval. suppose a…

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.\nparty affiliation\n| |republican|democrat|independent|total|\n|--|--|--|--|--|\n|do you approve of the mayors job performance|approve|0.14|0.25|0.03|0.42|\n| |disapprove|0.22|0.1|0.12|0.44|\n| |no opinion|0.03|0.07|0.04|0.14|\n|total|0.39|0.42|0.19|1|\nsample problem\np(approve)\ni can look at the value in the total column and approve row to determine p(approve).\n0.42\np(independent or disapprove)\n> enter the answer in the space provided. use numbers instead of words.

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.\nparty affiliation\n| |republican|democrat|independent|total|\n|--|--|--|--|--|\n|do you approve of the mayors job performance|approve|0.14|0.25|0.03|0.42|\n| |disapprove|0.22|0.1|0.12|0.44|\n| |no opinion|0.03|0.07|0.04|0.14|\n|total|0.39|0.42|0.19|1|\nsample problem\np(approve)\ni can look at the value in the total column and approve row to determine p(approve).\n0.42\np(independent or disapprove)\n> enter the answer in the space provided. use numbers instead of words.

Answer

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