Homework 15: Problem1 Previous Problem List (/webwork2/wardSTAT22 user leonel r
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Homework 15: Problem1 Previous Problem List (/webwork2/wardSTAT22 user leonel r kafando%40GeorgiaSouthern edu&effectiveUser-leonel; r kafando%40GeorgiaSouthern ed Next (webwork2/wardSTAT2231F2 leonel r kafando%40GeorgiaSouthernedu&effectiveUser-leonel; r_kafando%40GeorgiaSoutherner user (1 point) In a survey of 276 people, the following data were obtained relating gender to political orientation: Republican (R) Democrat (D)independent ()Total Male (M) Female (F) Total 100 52 152 40 51 91 13 153 123 276 20 A person is randomly selected. What is the probability that the person is: a) Male? b) Male and a Democrat? c) Male given that the person is a Democrat? d) Republican given that the person is Male? e) Female given that the person is an Independent? f) Are the events Female and Independent independent? Enter yes or no Note: You can earn partial credit on this problem. Preview My Answers Submit Answers You have attempted this problem 0 times. You have unlimited attempts remaining. Email instructorExplanation / Answer
a) Probability that the person is male
= Number of males / Total number of people
= 153 / 276
= 0.5543
Therefore 0.5543 is the required probability here.
b) Probability that the person is a male and a democrat is computed as:
= Number of males that are democrats / Total number of people
= 40/276
= 0.1449
Therefore 0.1449 is the required probability here.
c) Given that the person is a democrat, probability that the person is male is computed as:
= Total number of males that are democrats / Total number of democrats
= 40 / 91
= 0.4396
Therefore 0.4396 is the required probability here.
d) Given that the person is a male, probability that the person is a republican is computed as:
= Total number of males that are republican / Total number of males
= 100 / 153
= 0.6536
Therefore 0.6536 is the required probability here.
e) Given that the person is independent, probability that person is a female is computed as:
= Probability that a person is a female and independent / Total number of independent persons
= 20/ 33
= 0.6061
Therefore 0.6061 is the required probability here.
f) P( female ) = 123 / 276 = 0.4457
P( independent ) = 33 / 276 = 0.1196
P( female and independent ) = 20 / 276 = 0.0725
Also, P( female ) P( independent ) = 0.4457*0.1196 = 0.0533
Therefore, P( female ) P( independent ) is not equal to P( female and independent ) and therefore the 2 events are not independent.
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