2. Last year, at Southern Manufacturing Co., 270 people had colds during the yea

Question

2. Last year, at Southern Manufacturing Co., 270 people had colds during the year. One hundred eighty people who did no exercising had colds, and the remainder of the people with colds were involved in a weekly exercise program. 42% of the 1,000 em!ployees were involved in some type of exercise a) Complete the following table in terms of number of people. The letters in parenthesis refer to the name defined for the events Exercise (E No Exercise (F) Total Cold (C) No Cold (D) Total Do not forget to use the event notation while answering the following questions: b) What is the probability that an employee will have a cold next year? Show your work c) What is the probability that an employee wi have a cold or exercise next year? d) Given that an employee is involved in an exercise program, what is the probability that he or she will get a cold next year? Show your work! e) What is the probability that an employee who is not involved in an exercise program will not get a cold next year? Show your work! f) Are exercising and getting a cold independent events? Explain your answer

Explanation / Answer

b) P(C) =270/1000 =0.27

c) P(E U C) =(90+330+180)/1000 =0.6

d) P(C|E) =90/420 = 0.2143

e) P(D|F) =400/580 =0.6897

f)

as P(E)*P(C) =(420/1000)*(270/1000)=0.1134

and P(E &C) =90/1000 =0.09

as they both are not equal therefore excercise and getting cold are nt independent.

Exercise (E ) No exercise(F) Total Cold(C ) 90 180 270 No cold (D ) 330 400 730 Total 420 580 1000

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