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 do you approve of the mayors job performance approve 0.14 0.25 0.03 0.42 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(republican or approve) > enter the answer in the space provided. use numbers instead of words.

Explanation:

Step1: Recall the formula for $P(A\ or\ B)$

$P(A\ or\ B)=P(A)+P(B)-P(A\ and\ B)$
Let $A$ be the event of being a Republican and $B$ be the event of approving.

Step2: Find $P(\text{Republican})$

From the table, $P(\text{Republican}) = 0.39$

Step3: Find $P(\text{approve})$

From the table, $P(\text{approve})=0.42$

Step4: Find $P(\text{Republican and approve})$

From the table, $P(\text{Republican and approve}) = 0.14$

Step5: Calculate $P(\text{Republican or approve})$

$P(\text{Republican or approve})=0.39 + 0.42- 0.14$
$P(\text{Republican or approve})=0.67$

Answer:

$0.67$