Question

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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 probability that a randomly selected employee works both part time and 5 days each week?

Answer 1

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.

Answer 2

P(A and B)= P(A) *P(B) = 0.14*0.8 = 0.112
I did do the same your but the key not match
The key is 0.02

Answer 3

I see the problem. You don't want to use that equation, P(A and B) = P(A)*P(B) to find the intersection unless you know that the two events A and B are independent.
Go back to the formula for the union, P(A U B) = P(A) + P(B) - P(A and B)
You know P(AUB) = 0.92 and you know P(A) = .14 and P(B) = 0.80
So you can write the Union formula as 0.92 = 0.14 + 0.80 - P(A and B)
Since P(A and B) is the only thing you don't know, you can solve for it.
Combine the numbers on the right side:
0.92 = 0.94 - P(A and B
Add P(A and B) to both sides:
P(A and B) + 0.92 = 0.94
Subtract 0.92 from both sides:
P(A and B) = 0.94 - 0.92 = 0.02
I believe that is the answer you are looking for. Does it make sense how I got there?

Answer 4

Thanks you very much

Answer 5

You're welcome!

Answer 6

I appreciate the medal :)