Out of 100 employees at a company, 92 employees either work part time or work 5 days each week. There are 14 employees who work part time and 80 employees who work 5 days each week. What is the probability that a randomly selected employee works both part time and 5 days each week?

Answer: 0.02

Step-by-step explanation:

OpenStudy (judygreeneyes):

Hi - If you are working on this kind of problem, you probably know the formula for the probability of a union of two events. Let's call working part time Event A, and let's call working 5 days a week Event B. Let's look at the information we are given. We are told that 14 people work part time, so that is P(A) = 14/100 - 0.14 . We are told that 80 employees work 5 days a week, so P(B) = 80/100 = .80 . We are given the union (there are 92 employees who work either one or the other), which is the union, P(A U B) = 92/100 = .92 .. The question is asking for the probability of someone working both part time and fll time, which is the intersection of events A and B, or P(A and B). If you recall the formula for the probability of the union, it is

P(A U B) = P(A) +P(B) - P(A and B).

The problem has given us each of these pieces except the intersection, so we can solve for it,

If you plug in P(A U B) = 0.92 and P(A) = 0.14, and P(B) = 0.80, you can solve for P(A and B), which will give you the answer.

I hope this helps you.

Credit: https://questioncove.com/updates/5734d282e4b06d54e1496ac8

Answer:

The probability that a randomly selected employee works both part time and 5 days each week is 0.02

Step-by-step explanation:

What is probability?

Probability is a branch of math which deals with finding out the likelihood of the occurrence of an event.

The total employees =100

Let A= Employees who work part time = 14

and B = Employees who work 5 days each week = 80

Then, A∪B= 92

We have to find, P(A∩B)

P(A∪B)=P(A)+P(B)-P(A∩B)

[tex]\frac{92}{100}=\frac{14}{100}+\frac{80}{100}-[/tex]P(A∩B)

0.92=0.14+0.8-P(A∩B)

0.92=0.94-P(A∩B)

P(A∩B)=0.02

Hence, the probability that a randomly selected employee works both part time and 5 days each week is 0.02.

To know more about probability here

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