**Please provide full calculations to give understanding of problem (A-D)** Last
ID: 3306514 • Letter: #
Question
**Please provide full calculations to give understanding of problem (A-D)** Last year, at Northern Manufacturing Company, 200 people had colds during the year. One hundred fifty five people who did no exercising had colds, and the remainder of the people with colds were involved in a weekly exercise program. Half of the 1,000 employees were involved in some type of exercise. (a) What is the probability that an employee will have a cold next year? (b) Given that an employee is involved in an exer- cise program, what is the probability that he or she will get a cold next year? (c) What is the probability that an employee who is not involved in an exercise program will get a cold next year? (d) Are exercising and getting a cold independent events? Explain your answer.Explanation / Answer
a) P(an employee having cold) = Number of employees who got cold / Total employess = 200/1000 = 0.2
b) P(Employee gets cold | Involved in exercise program)
= Number of employees who got cold and exercise / Total employees who exercise
= 45/500 = 0.09
c) P(Employee gets cold | Not involved in exercise program)
= Number of employees who got cold and do not exercise / Total employees who do not exercise
=155/500 = 0.31
d) Events A and B are independent if the equation P(AB) = P(A) P(B) holds true.
P(Exercising) = 0.5, P(gets cold) = 0.2, P(Exercising and Cold) = 45/1000 = 0.045
0.5*0.2 is not equal to 0.045, Therefore the events are not independent
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