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# Probability Problem

Suppose that 18% of the employees at a given corporation engage in physical exercise activities during the lunch hour. Moreover, assume that 57% of all employees are male, and 12% of all employees are males who engage in physical exercise activities during the lunch hour.

a)if we choose an employee at random from this corporation, what is the probability that this person is a female that engages in physical exercise activites during the lunch hour?

b)if we choose an employee at random from this corporation, what is the probability that this employee is a female that does not engage in physical exercise activities during the lunch hour?

#### Solution Preview

The simplest way to attack this problem is to assume there are 100 employees (for ease of converting to percentages later).

The problem states that 18% of employees engage in exercise at lunch. So, 18 of our 100 employees exercise at lunch.

The problem states that 57% of the ...

#### Solution Summary

The problem describes a workplace where a certain percentage exercise, a certain percent are women, a certain percent are men, etc creating overlapping pools of persons, of which you are asked to calculate the probability that a randomly selected person from the group is XYZ.

The solution is detailed with an attached tree breaking down the catergories for simplicity.

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