The table below summarizes results from a study of people who refused that the s

Question

The table below summarizes results from a study of people who refused that the selected person refused to answer? Does the probablity value suggest that refusals are a problem for pollsters? to answer survey questions. If one of the subjects is randomly selected, what is the probablity Age 18-21 22-29 30-39 4049 50-59 60 and over 259 Responded 77 Refused 249 140 142 59 The probability that a randomly selected person refused to answer is (Do not round until the final answer. Then round to three decimal places as needed.) Does the probability value suggest that refusals are a probiem for polisters? A. O B. c. 0 D. Yes, the refusal rate is above 10%. This results in a sample size that is too small to be useful. No, the refusal rate is below 10%. This ensures that a suitable number of people were sampled. Yes, the refusal rate is above 10%. This may suggest that the sample may not be representative of the population. No, the refusal rate is below 10%. The sample wil likely be representative of the population.

Explanation / Answer

1) From the given table, the total number of people to be surveyed = 1267

                                           Total number of people who responded to answer the survey question = 1073

                                And the total number of people who refused to answer the survey question = 194

Therefore, the probability that a randomly selected person refused to answer P(Refused) is

P(Refused)=(Total number of people who refused to answer survey question)/( total number of people to be surveyed)

P(Refused) = 194/1267 = 0.153118

Therefore, the probability that a randomly selected person refused to answer = 0.153

The probability of refusal is greater than 10% and since the peoples who refuse to answer the question are belonging to different age groups and they have different opinions, therefore, the sample may not be representative of the population

2) The image is not clearly taken. The number of false-positive results is not seen in the image.

3) Since the event A or B indicates that the event A occurs or B occurs or Both occurs. Therefore, the probability of A or B is same as the probability A occurs or B occurs or both occurs. Hence the answer is the second option that is

P(A or B) indicates the probability that in a single trial, event A occurs, event B occurs, or they both occurs.

4)

A: When a page is randomly selected and ripped from a 12-page document and destroyed, it is page 4.

B: When a different page is randomly selected and ripped from the document, it is page 8.

The documents contain 12 pages and suppose event A occurs then one page is ripped from the document. Hence the document contains 11 pages. And the probability of event A occurs is 1/12. If event A occurs then the document contains 11 pages and therefore the probability of event B occurs is 1/11. Hence if event A occurs then it affects on the probability of occurrence of event B and vice-versa.

Therefore, the event A and B are dependent because the occurrence of one event affects the probability of the occurrence of the other event.

The probability that the event A and B both occurs = P(A)*P(B)= (1/12)*(1/11)=1/132=0.007575

Hence, the probability that the event A and B both occurs is 0.0076.

5)

A: When a baby is born, it is a girl.

B: When a 12-sided die is rolled, the outcome is 12.

Since the occurrence of an event A that is, when a baby is born and it is a girl then it is not affected on the occurrence of event B i.e. on the occurrence of 12 from 12 sided die and vice versa.

Therefore event A and B are independent because the occurrence of one event affects the probability of the occurrence of the other event.

When a baby is born then either it is a boy or a girl then the probability of a girl = 1/2 =0.5

That is, P(A)=1/2=0.5

When a 12 sided die is rolled then there are 12 outcomes which are 1,2,3,4,5,6,7,8,9,10,11,12.

The occurrence of 12 is 1/12 =0.08333

That is, P(B) = 1/12 = 0.08333

As event A and B are independent therefore

P(A and B) = P(A)*P(B) = (1/2)*(1/12) = 1/24 = 0.041666

Therefore, the probability that events A and B both occurs is 0.04167.

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