A small manufacturing company has rated
80% of its employees as satisfactory and 20% as unsatisfactory . Personnel records show that 75% of the satisfactory workers had previous work experience in the job they are now doing, while 30% of the unsatisfactory workers had no work experience in the job they are now doing. If a person who has had previous work experience is hired, what is the approximate probability that this person will be an unsatisfactory employee?
I just need the ratio and the process of getting the answer Thanks!
Well, let's break it down step by step. We know that 80% of employees are rated as satisfactory, so that means 20% are unsatisfactory. Out of the satisfactory workers, 75% had previous work experience in the job, so that leaves 25% without previous work experience. Out of the unsatisfactory workers, 30% had no work experience in the job.
Now, if we hire a person with previous work experience, we want to find the approximate probability that this person will be unsatisfactory. We can use conditional probability to calculate this.
The conditional probability formula is: P(A|B) = P(A ∩ B) / P(B), where P(A|B) is the probability of event A occurring given that event B has already occurred, P(A ∩ B) is the probability of both A and B occurring, and P(B) is the probability of event B occurring.
In this case, A represents a person being unsatisfactory and B represents a person having previous work experience. We want to find P(A|B), the probability of a person being unsatisfactory given that they have previous work experience.
Let's plug in the numbers:
P(A ∩ B) = 20% (since 20% of employees are unsatisfactory)
P(B) = 75% (since 75% of satisfactory workers have previous work experience)
Now, we can calculate:
P(A|B) = P(A ∩ B) / P(B)
P(A|B) = 20% / 75%
P(A|B) ≈ 26.67%
Therefore, the approximate probability that a person with previous work experience will be an unsatisfactory employee is approximately 26.67%.
Now, I hope this answer satisfies you!
To find the approximate probability that a person with previous work experience will be an unsatisfactory employee, we can use the following steps:
Step 1: Assign variables
Let's assign the following variables:
S: Satisfactory employee
U: Unsatisfactory employee
W: Previous work experience
NW: No previous work experience
We are given the following information:
P(S) = 0.80 (probability of being satisfactory)
P(U) = 0.20 (probability of being unsatisfactory)
P(W | S) = 0.75 (given that a person is satisfactory, probability of having previous work experience)
P(NW | U) = 0.30 (given that a person is unsatisfactory, probability of not having previous work experience)
Step 2: Find the probability of having previous work experience
To find the probability of having previous work experience (P(W)), we can use the law of total probability:
P(W) = P(W | S) * P(S) + P(W | U) * P(U)
= 0.75 * 0.80 + 0 * 0.20 (since P(W | U) = 0.30 and P(U) = 0.20)
= 0.60
Step 3: Find the probability of being an unsatisfactory employee given previous work experience
To find the probability of being an unsatisfactory employee given previous work experience (P(U | W)), we can use Bayes' theorem:
P(U | W) = (P(W | U) * P(U)) / P(W)
= (0 * 0.20) / 0.60 (since P(W | U) = 0.30 and P(U) = 0.20)
= 0
Therefore, the approximate probability that a person with previous work experience will be an unsatisfactory employee is 0.
To solve this problem, we can use conditional probability. We are given that 80% of the employees are satisfactory and 20% are unsatisfactory. Additionally, we know that 75% of the satisfactory employees have previous work experience, and 30% of the unsatisfactory employees do not have work experience.
Let's use some letters to represent the events:
- S represents the event that an employee is satisfactory.
- U represents the event that an employee is unsatisfactory.
- E represents the event that an employee has previous work experience.
We are asked to find the probability of an employee being unsatisfactory given that they have previous work experience, which can be written as P(U|E). This can be calculated using the formula for conditional probability:
P(U|E) = P(U ∩ E) / P(E)
To find P(U ∩ E), we can multiply the probabilities of being unsatisfactory and having previous work experience:
P(U ∩ E) = P(U) * P(E)
We are given that P(U) = 0.20 and P(E|U) = 0.30.
To find P(E), we can use the law of total probability:
P(E) = P(E|S) * P(S) + P(E|U) * P(U)
We are given that P(E|S) = 0.75 and P(S) = 0.80.
Now, let's calculate the values:
P(U ∩ E) = P(U) * P(E) = 0.20 * (P(E|S) * P(S) + P(E|U) * P(U))
P(E) = P(E|S) * P(S) + P(E|U) * P(U) = 0.75 * 0.80 + 0.30 * 0.20
Finally, we can calculate P(U|E):
P(U|E) = P(U ∩ E) / P(E)
Now, you can substitute the values into the formula to find the approximate probability that a person with previous work experience will be an unsatisfactory employee.