Calculating Probability of Division Manning Decrease

[iNCREDiBLE]

I'm new to this, so can someone please explain how this problem is solved:

What is the probability that your divisions manning will decrease given that corporation's retention rate?

Corporation retention figures for first-term (0-4 years), second-term (4-8 years), and third-term contracts (8-12 years) were 30%, 46%, and 54% respectively.

Personnel within the division is:
10 first-term individuals
12 second-term individuals
10 third-term individuals

We know the corporations retention figures as they have already occurred, now...what is the probability of attrition within a division within the corporation with regards to this additional information?

 

[OlderDan]

I'm new to this, so can someone please explain how this problem is solved:

What is the probability that your divisions manning will decrease given that corporation's retention rate?

Corporation retention figures for first-term (0-4 years), second-term (4-8 years), and third-term contracts (8-12 years) were 30%, 46%, and 54% respectively.

Personnel within the division is:
10 first-term individuals
12 second-term individuals
10 third-term individuals

We know the corporations retention figures as they have already occurred, now...what is the probability of attrition within a division within the corporation with regards to this additional information?

In each category, an individual either leaves the company or stays with the company with a probability that is known from the retention statistics. You can find the probability of retaining every individual in the division from the product of the probabilities of retaining each of them. The probability of attrition is 1 minus the probability that nobody leaves. If you have studied the binomial distributiuon, you can also treat this problem as a combination of three binomial problems. The probability that all individuals within one category in your division are retained depends on the number of such individuals and the probability of retaining such an individual.

 

[thepatientmental]

To calculate the probability of division manning decreasing, we need to first understand the information given. The corporation's retention rate refers to the percentage of employees who choose to stay with the company for a certain length of time. In this case, the retention rates for first-term, second-term, and third-term contracts are 30%, 46%, and 54% respectively. This means that out of all the employees in each contract category, only 30%, 46%, and 54% of them will stay with the company for the designated time period.

Next, we are given the number of personnel in the division, broken down by contract term. There are 10 first-term individuals, 12 second-term individuals, and 10 third-term individuals. To calculate the probability of division manning decreasing, we need to determine the likelihood that any of these individuals will leave the company.

Using the given retention rates, we can calculate the probability of each individual staying in the company. For first-term individuals, the probability of staying is 30%, for second-term individuals it is 46%, and for third-term individuals it is 54%. Therefore, the probability of any individual leaving the company would be the complement of these probabilities, which is 70%, 54%, and 46% respectively.

To calculate the overall probability of division manning decreasing, we can multiply these individual probabilities together. This is because the probability of all individuals staying with the company is the product of their individual probabilities.

So, the probability of division manning decreasing can be calculated as follows:

Probability = (Probability of first-term individual leaving) x (Probability of second-term individual leaving) x (Probability of third-term individual leaving)
= (0.70) x (0.54) x (0.46)
= 0.17964 or approximately 18%

Therefore, there is a 18% chance that the division's manning will decrease based on the given information about the corporation's retention rates and the number of personnel in the division. It is important to note that this is only a prediction and the actual probability may vary depending on other factors.