Last year at Northern Manufacturing Company 200 people had c

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 exercise program, what is the probability that he or she will get a cold next year?

Solution

Number of people doing exercise = 500

People not doing exercises = 500

Now, we assume that the number of people getting colds will follow the same probability distribution as this year.

Hence :

P ( Cold | No exercise) = 155 / 500 = 0.31

P ( Cold | Exercise ) = (200 - 155) / 500 = 45 / 500 = 0.09

P ( No Cold | Exercise ) = ( 500 - 45 ) / 500 = 0.91

P( No Cold | No Exercise ) = (500 - 155) / 500 =0.69

Thus,

P ( Cold ) = P ( Exercise | Cold ) + P ( No Exercise | Cold ) = 200 / 1000 = 20 %

and

P ( Cold | Exercise ) = (200 - 155) / 500 = 45 / 500 = 0.09