Question

Sara is reviewing recent orders at her deli to determine which meats she should order. She found that of 1,000 orders, 390 customers ordered turkey, 345 customers ordered ham, and 200 customers ordered neither turkey nor ham. Based on these data, how many of the next 1,000 customers will order both turkey and ham? Show your work and use complete sentences.
@mathmale

Answer 1

We obtain empirical probabilities from the given data. If 390 out of 1000 customers order turkey, then the probability that a customer will order turkey is 390/1000. Likewise, the empirical probability that a customer will order ham is 345/1000, and that that a customer will order neither turkey nor ham is 200/1000.

Are you familiar with Venn diagrams?

Answer 2

yes i am

Answer 3

Draw a nice rectangle which supposedly contains all 1000 customers (not literally, of course). Divide it up: about 0.390 of the area of that rectangle represents the fraction of 1000 customers who will order turkey. Another, separate area which is about 0.345 of the whole area will order ham. What are the 3rd and 4th areas to draw?

Answer 4

and what do they represent?

Answer 5

i mean both ham and turkey

Answer 6

That's a good decision. It's entirely possible that a customer could order both ham and turkey on his sandwich; I do that all the time.
Add up .390, .345 and .200. What's the sum?

Answer 7

.935?

Answer 8

And if you subtract that sum from 1.000, what do you get (what numeric value)?

Answer 9

.065

Answer 10

And what do you think that fraction represents?

Answer 11

idk

Answer 12

Look at what the other areas repr.:
.390: prob. that cust. will choose turkey alone
.345: prob. that cust. will choose ham alone
.200: prob that cust will choose neither ham nor turkey
.065: ???
1.000 total

Answer 13

i dont understan what your asking like .065 would look like a fraction? @mathmale

Answer 14

0.065 is a fraction, just like .390, .345 and .200. think carefully about what .390, .345 and.200 represent: they are both percentage areas and probabilities.
Stretch your undrstanding to cover that .065; what could that possibly represent? Please go back and re-read the original problem.

Answer 15

Have you drawn and labelled a Venn Diagram as I suggested you do earlier?

Answer 16

6.5% perfer ham and turkey?

Answer 17

If it helps any: remember that the sum of all the probabilities of the events possible is always 1. Yes, that's right. Dummies like me like both ham and turkey on their sandwiches.

Answer 18

So again, if you add up the probabilities that a customer will choose
turkey only
ham only
neither ham nor turkey
both ham and turkey

these probabilities MUST add up to what?

Answer 19

I'm always reviewing things in the hope that this will help you to remember them. Look at my previous post; the answer to my question is there.

Answer 20

woohoo? Please respond in some way, even if only to say idk.

Answer 21

I need to hit the sack really soon.
Empirical probability is based upon observations. We sampled 1000 customers and by actual counting found that of those, 390 would choose turkey, 345 ham, 200 neither ham nor turkey, and the remainder of those 1000 both ham and turkey. Thus, the empirical probability that a customer chosen at random will choose both ham and turnkey is .065.

Answer 22

brb

Answer 23

If we're talking about the next 1000 customers, and want to know how many of those will probably choose both ham and turkey, all we have to do is to multiply that number (1000) by the probability P(ham and turkey). that's the answer you want.

Answer 24

Please review this conversation and then write a short essay, using complete sentences, perhaps a Venn diagram, probability values, numbers of customers, etc., to explain how you have estimated the number of the next 1000 customers who will order both ham and turkey on their sandwiches.

woohoo, I'm sorry, but I had intended to hit the sack at about the time you found me online about 35 minutes ago. If and when we "meet" online, I'd hope we'd each make this dialogue our first priority (over everything else). I don't know what has drawn your attention away from this problem solving, and hope it wasn't an emergency.

You may, of course, post other problems, but I won't see them until tomorrow.
Glad to "see" you again online. good night! MM

Answer 25

nooo dont leave plsss

Answer 26

It's 5:20 a.m. out here in California. Let me know what time frame or frames today would work for you to continue our discussion.