2. A new restaurant has five (5) entrees. For the first week, the owner assumes
ID: 3317550 • Letter: 2
Question
2. A new restaurant has five (5) entrees. For the first week, the owner assumes that o entrée choice will be equally likely and orders food accordingly. At the end of the week, data on entrée orders are compiled, as shown in the table below. rders of each Probability entrée will Entrée Orders Vegetarian be ordered E1 E2 E3 E4 18 Yes ES 17 No 10 No 22 Yes 33 No Think about the following as an experiment: A customer will come to the restaurant next week and choose an entrée from the restaurant menu. What is the sample space S? a. b. On the chart, fill in your estimate of the probability of each entrée being ordered by a future customer What method did you use to assign these probabilities? Did you check the properties? c. Was the owner correct when he assumed that the entrees were equally likely to be chosen during the first week correct? Explain BRIEFLY d. e. Let A be the event Vegetarian Meals. what entrees are in A? A = { ii. Describe A as union of elementary events: A-Explanation / Answer
(a) There are 5 possible entrees in the restraunt menu. So a new customer will have to choose one from the 5 entrees. Hence the sample space is of size 5 and is {E1, E2, E3, E4, E5}
(b) We have for each entree the number of times it has been ordered in a week. So we apply the Theorem of Classical probability to find the probability of each entree being ordered.
We assume that each of the entree is equally likely and hence the probabiloty of each entree is the number of times the entree has been ordered divided by the total number of orders in the first week = 100
The table of probabilities is attached below.
(c) We assumed the method of Definitipon of Classical probability where we actually assumed that the 5 entrees in the menu are equally likely to be chosen. The other assumptions that they are exclusive and exhaustive are alreday satisfied by the design of the problem. The assumption of equally likley is guranteed by the owner who tells to assume that the entrees are equally likely to be selected.
(d) Equally likely is a part of the definition but in turn it gives rise to probability. Equally likely and equally probable are very similar terms and hence there is a circularity in the definition of probability. However the probabilities of the 5 entrees that we see are not all equal. Entree 3 has been selected much more than the other entree. So the owner is not right in assuming that the entree are equally lkely / equally probable.
<Have answered the first 4 subparts as per the answering guidelines>
Entrée Number of Orders Prob E1 10 0.1 E2 22 0.22 E3 33 0.33 E4 18 0.18 E5 17 0.17 Total 100Related Questions
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