Question

In the department of labor, 70% of the employees are male, 30% are female, and 35% of the employees have business degrees. Of those having business degrees, 40% are female. Calculate the following probabilities: a. A randomly selected employee is a female with a business degree. b. A randomly selected male has a business degree.

Answer 1

The probability of a female with a business degree is 14%, while the probability that a randomly selected male has a business degree is 21%, based on the given percentage of employees with business degrees and their gender distribution.

Step-by-step explanation:

In this probability question, we are asked to calculate two different probabilities based on given statistics from a department of labor.

• Probability of a female with a business degree: Since 35% of employees have business degrees and 40% of those with business degrees are female, we multiply these probabilities (0.35 * 0.40) to find that 14% of all employees are females with a business degree.
• Probability a randomly selected male has a business degree: To calculate this, we need to determine the percentage of business degree holders who are male. If 40% of business degree holders are female, then 60% are male. So, 35% of all employees are business majors, and 60% of those are male, which gives us 0.35 * 0.60 = 21% as the probability that a randomly selected male has a business degree.

These calculations are made simpler by breaking down the given percentages and creating relationships between the different groups within the employee population.