answer all parts please A group of students in a statistics class gathered data

Question

answer all parts please

A group of students in a statistics class gathered data on MSU students' GPA, gender, age, and marital, student, and employment status. You will use their data for much of the remaining exam. 3. The table below contains data about the marital status and employment status of a group of MSU students. (3 pts each 21 pts) Marital Status and Employment Status Married Total Unemployed Total 34 168 202 Full-timne Part-time 20 26 106 120 42 56 For a-g, please leave your answers in unreduced fraction form. Do not convert to decimals. A student is chosen at random. Find the probability that the student: Is married, P(married). a. b. Is married, given he or she is unemployed, P(married I unemployed) c. Works full-time or part-time, P(full-time or part-time). d. Works full-time, given he or she is single, P(full-time | single). e. Works part-time and is married, P(part-time and married). f. Not working fulltime, Pnot full-time). g Are the events "part-time" and "married" independent? Justify your answer mathematically.

Explanation / Answer

A) P(married) = 34/202 = 17/101

B) P(married | unemployed) = P(married and unemployed) / P(unemployed)

= (14/202)/(56/202)

= 14/56

= 1/4

C) P(full time or part time) = P(full time) + P(part time)

= 26/202 + 120/202

= 73/101

D) P(full time | single) = P(full time and single) / P(single)

= (20/202)/(168/202)

= 20/168

= 5/42

E) P(part time and married) = 14/202 = 7/101

F) P(not full time) = 1 - P(full time)

= 1 - 26/202

= 94/101

G) P(part time) = 120/202 = 60/101

They are not independent, because P(part time and married) is not equal to P(married) *P(part time)

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