Employees at company X, Male Academics = 40; Support Male Staff = 10 and Female Academics = 80 and Support Female Staff = 20.
If an employee is selected at random, the probability that the employee is:
1. Female
2. Not an academic staff
3. Not female and not support staff
4. Male or academic staff
5. Male, given that he is an academic staff
To find the probabilities, we need to first calculate the total number of employees in each category and then divide that by the total number of employees in the company (which we assume to be the sum of all the categories).
Total employees:
Male Academics = 40
Support Male Staff = 10
Female Academics = 80
Support Female Staff = 20
1. Probability that the employee is female:
Female Academics + Support Female Staff = 80 + 20 = 100.
Therefore, the probability that the employee is female is 100/(40 + 10 + 80 + 20) = 100/150 = 2/3 or 0.67.
2. Probability that the employee is not an academic staff:
Support Male Staff + Support Female Staff = 10+ 20 = 30.
Therefore, the probability that the employee is not an academic staff is 30/(40 + 10 + 80 + 20) = 30/150 = 1/5 or 0.2.
3. Probability that the employee is not female and not part of the support staff:
Male Academics + Female Academics = 40 + 80 = 120.
Therefore, the probability that the employee is not female and not part of the support staff is 120/(40 + 10 + 80 + 20) = 120/150 = 4/5 or 0.8.
4. Probability that the employee is male or an academic staff:
Male Academics + Support Male Staff = 40 + 10 = 50.
Therefore, the probability that the employee is male or an academic staff is 50/(40 + 10 + 80 + 20) = 50/150 = 1/3 or 0.33.
5. Probability that the employee is male, given that he is an academic staff:
We need to find the probability of being male and being an academic staff and divide it by the probability of being an academic staff.
The probability of being male and an academic staff is Male Academics / (Male Academics + Female Academics) = 40 / (40 + 80) = 40/120 = 1/3 or 0.33.
The probability of being an academic staff is (Male Academics + Female Academics) / (40 + 80 + 10 + 20) = 120/150 = 4/5 or 0.8.
Therefore, the probability that the employee is male, given that he is an academic staff is (1/3) / (4/5) = (1/3) * (5/4) = 5/12 or 0.42.