1. Of all employees, 20% left the organisation last year, and 7% did not
complete mandatory training and left. Given that an employee left, what
is the probability that they did not complete the training?
2. In a company, 30% of employees are rated as “high-performers.” Given
that the employee is a high performer, the person has an 80% chance of
getting promoted. What is the probability that a randomly selected
employee is a high-performer and also promoted?
3. In a company, the probability of an employee completing diversity
training is 0.6. The probability that an employee works remotely is 0.5.
The probability that an employee has completed diversity training and
works remotely is 0.3. Are the events, training completion and remote
work independent?
4. In a large company with many employees, the HR department tracks two
independent events: an employee successfully completes a training
program, and an employee attends a workshop. The probabilities of the
two events are, respectively, 0.7 and 0.9. Find
i.
The probability of an Employee Completing Training and attending a
Workshop.
ii.
Probability of an Employee Completing Training or Attending a
Workshop (or both)
5. A company is hiring for three positions: a software engineer, a data
analyst, and a project manager. Based on the current applicant pool, the
HR department has estimated the probability of selecting a qualified
software engineer is 0.6, the probability of selecting a qualified data
analyst is 0.5, and the probability of selecting a qualified project manager
is 0.7. Assume that the selections for these positions are independent
events. What is the probability that the company will successfully hire
qualified candidates for all three positions? What is the probability that
the company will hire at least one qualified candidate for the three
positions?
6. A company conducts training sessions for its employees in leadership,
technical skills, and communication. The HR department estimates the
following probabilities for an employee to complete each training
successfully from past data. The probability of completing leadership
training is 0.8, the probability of completing technical skills training is
0.9, and the probability of completing communication training is 0.85.
Assume the completion of each training is an independent event. How
likely is an employee to successfully complete all three training sessions?
How likely is an employee to complete at least one of the three training
sessions?
7. Employees in a company can enrol in three benefits: health insurance,
retirement plan, and gym membership. The HR department has observed
the following probabilities of an employee enrolling in these benefits.
The probability of enrolling in health insurance is 0.75, the probability of
enrolling in a retirement plan is 0.6, and the probability of enrolling in a
gym membership is 0.4. Assume that the enrollment in each benefit is an
independent event. What is the probability that an employee will enrol in
all three benefits? What is the probability that an employee will enrol in
at least one of the three benefits?
8. In a company, the probability of an employee being promoted to a senior
position is 0.3. Given that an employee is promoted, the probability of
being assigned to a key project is 0.5. If an employee is promoted and
assigned to a key project, the probability of receiving a significant bonus
is 0.8. What is the probability that an employee is promoted, assigned to a
key project, and receives a significant bonus?
9. An employee’s probability of completing an initial training program is
0.7. Given that an employee completes the initial training, the probability
that they will complete an advanced training program is 0.6. If an
employee completes the initial and advanced training programs, the
probability of obtaining certification is 0.9. What is the probability that an
employee completes the initial and advanced trainings and obtains
certification?
10. The probability that a new employee stays with the company for at least
one year is 0.7. Given that an employee stays for at least one year, the
probability that they will stay for an additional year is 0.8. If an employee
stays for two years, the probability that they will stay for a third year is
0.85. What is the probability that a new employee stays with the company
for three years?
11. A company’s employees are divided into three experience levels: Junior,
Mid-level and Senior. 40% of employees are at the junior level, while
35% and 25% are at the mid and senior levels, respectively. The
probability of getting promoted in a given year based on experience level
is 10%, 30%, and 50% for Junior, mid and senior levels. What is the
overall probability that a randomly selected employee gets promoted this
year?
12. An employee may work in one of three departments: 30% of employees
in Sales 50% in Operations, and 20% in R&D. Resignation rates vary by
department, resignation rates are respectively, 12, 8 and 5 percents for
Sales, Operations and R&D. What is the probability that a randomly
selected employee will resign in the next year?
13. Employees are categorised by their prior experience with training: No
experience (20%), Some experience (50%), Extensive experience (30%).
Based on experience, the probability of successfully completing a new
training program is: No experience: 60%, Some experience: 80%,
Extensive experience: 95%. What is the probability that a randomly
chosen employee will successfully complete the training?
14. A company receives applications from two sources: 60% from internal
referrals, and the rest from external job portals. Historical data shows that
80% of referred candidates have a professional certification, and 50% of
external applicants have the same certification. A randomly selected
applicant has the certification. What is the probability that this certified
applicant was referred internally?
15. In a company, 20% of employees are classified as high performers (H),
50% as average performers (A), and 30% as low performers (L). The
probability of receiving a “Very Good” performance review depends on
the group. High performers have a 90% chance of receiving “Very Good,
Average performers have a 40% chance, and Low performers have a 10%
chance. An employee received a “Very Good” review. What is the
probability that this employee is a high performer?
16. Based on previous data, HR classifies employees into three risk
categories for attrition: High, medium and low risks, and 10%, 30% and
60% of employees, respectively, belong to these categories. Also, 70%,
30% and 5% of employees from these three categories, respectively,
leave within a year. An employee has left the company. What is the
probability that this employee was originally in the high-risk category?