Warehouse In Exercises 51-54, a warehouse employs 24 workers o...

Question

Warehouse In Exercises 51-54, a warehouse employs 24 workers on first shift, 17 workers on second shift, and 13 workers on third shift. Eight workers are chosen at random to be

interviewed about the work environment.

Find the probability of choosing four third-shift workers.

Accepted Answer

Hello there. Today we're going to solve the following practice problem together. So first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. A company has 18 employees in the sales department, 14 in marketing, and 11 in engineering. If 6 employees are randomly chosen to attend day training, what is the probability that exactly 2 are from engineering? Awesome. So it appears for this particular problem we're ultimately asked to determine what the probability is that exactly 2 out of the 6 employees that are randomly chosen to attend this specific training are from the engineering department. So now that we know that we're ultimately trying to determine this probability value, let's read off our multiple choice answers to see what our final answer might be. A is 0.4238. B is 0.3244. C is 0.2671, and finally, D is 0.1842. Awesome. So our first step is we need to add the total number of employees, so we need to determine that the total amount of employees at this company. So we need to take the 18 employees in the sales department and add the 14 that are in the marketing department and the 11 that are in the engineering department, and when we add all those 3 values together, you will find that it's equal to 43 total. Our second step now is we need to determine the number of ways to choose 6 employees from 43, which will be the combination of 43 taken as 6 at a time. So we could write this as a binomial coefficient, which a binomial coefficient is just a fancy way of writing the combination formula. So we need to take 43 chooses 6 or 43/6 is equal to 6 million. 96,454. And once again we're using the combination formula for 43 chooses 6, and when we do that we will get 6,96,454 as an answer. Our 3rd step is we need to determine the number of ways to choose 2 employees from the 11 in the engineering department, which will be the combination of 11 taken as 2 at a time. So we can write this also as a binomial coefficient where 11 chooses 2. Which will be equal to 55, once again, using the combination formula to solve for that answer, and when you use the combination formula, you will get an answer of 55. And our fourth step is we need to determine the number of ways to choose the remaining 4 employees from the other 32 employees, which will be the combination of 32 taken as 4 at a time. So writing this as a binomial coefficient as 32 chooses 4, and this will be equal to when you use the combination formula 35,960. Fantastic. So now, our 5th step is we need to multiply the results from steps 3 and 4 to get the number of favorable outcomes. So the number of favorable outcomes, which I'll call NFO, so the number of favorable outcomes is equal to 55 multiplied by 35,960. Which will give us an answer of 1,977,000. 800 So now our 6th and final step is we need to determine the probability, and we need to note that the probability P is equal to the number of favorable outcomes, which is equal to 1,977,000. 800 divided by the total number of outcomes, which is 6,96,454. And when we plug that into our calculator, we will find that it's equal to when we round to 4 decimal places, 0.3244. And that's it. That is our final answer. Hooray, we did it. And this corresponds to multiple choice answer letter B, which once again is 0.3244. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

Warehouse In Exercises 51-54, a warehouse employs 24 workers on first shift, 17 workers on second shift, and 13 workers on third shift. Eight workers are chosen at random to be
interviewed about the work environment.
Find the probability of choosing four third-shift workers.

Key Concepts

Probability

Combinations

Total Workers and Distribution

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