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Conditional Probability and Fisher's Exact Test

I need some help answering this conditional probability question:
The following table is based on a random sample of 100 employee in a large fortune 500 company
# of days a week one exercises

2 or fewer days 18 (Male) 12 (Female)
3 or more days 32(Male) 38 (Female)

a) If an employee is randomly chosen from the 100 employees represented in the table above, what is the probability that the chosen employee exercises 3 or more days a week (label A)?

b) If an employee is randomly chosen from the 100 employees represented in the table, what is the probability that the chosen employee exercises 3 or more days a week, given that the chosen employee is male ( label B)?

c) Are events A and B independent?

d) Use a chi-square to determine if gender and the number of days a week an employee exercises are independent at the .01 level of significance

Solution Preview

Solution:
a) Now A=number of people who exercises 3 or more days a week. From the give table, there are 32+38=70 people who exercises 3 or more days a week. Since there are 100 people together, P(A)=70/100=0.7

b) Using formula of conditional probability, P(people who exercises 3 or more days a week given male)=P(people who exercises 3 or more days a week and people who is male)/P(people who is male)
Now there are 18+32=50 ...

Solution Summary

The solution gives detail steps on calculating conditional probability and performing fisher's exact test. All formula and calculations are shown and explained.

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