Problem 2. Suppose out of 50 tables in a restaurant, 35 have a person who orderedwith his/her entree, 25 have a person who ordered salad with his/her entree, and 10 haveordered both.soup(a) How many tables will have neither a soup nor a salad delivered to them?(b) How many tables will only have a salad delivered?(c) What is the probability that a table will have a soup or a salad delivered?(d) What is the probability that a table will not have a soup delivered?(e) Are the events "soup delivered to the table" and "salad delivered to the table" mutu-ally exclusive? Are they independent? Justify your answers.

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Asked Nov 18, 2019
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Could you do question 2, d and e?

Problem 2. Suppose out of 50 tables in a restaurant, 35 have a person who ordered
with his/her entree, 25 have a person who ordered salad with his/her entree, and 10 have
ordered both.
soup
(a) How many tables will have neither a soup nor a salad delivered to them?
(b) How many tables will only have a salad delivered?
(c) What is the probability that a table will have a soup or a salad delivered?
(d) What is the probability that a table will not have a soup delivered?
(e) Are the events "soup delivered to the table" and "salad delivered to the table" mutu-
ally exclusive? Are they independent? Justify your answers.
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Problem 2. Suppose out of 50 tables in a restaurant, 35 have a person who ordered with his/her entree, 25 have a person who ordered salad with his/her entree, and 10 have ordered both. soup (a) How many tables will have neither a soup nor a salad delivered to them? (b) How many tables will only have a salad delivered? (c) What is the probability that a table will have a soup or a salad delivered? (d) What is the probability that a table will not have a soup delivered? (e) Are the events "soup delivered to the table" and "salad delivered to the table" mutu- ally exclusive? Are they independent? Justify your answers.

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Expert Answer

Step 1

Given data

Total tables n(T)= 50

No of persons who ordered soup, n(A) = 35

No of persons who ordered salad, n(B) = 25

No of persons who ordered both, n(A∩B) = 10

d)

Probability that the table will not have a soup delivered is given by

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n(A)n(B) - n(A n B)V P(A U B) 1- P(AUB) = 1 - п(T) 3525 10 = 1 - = 1 1 = 0 50 Probability that the table will not have a soup delivered is 0

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Step 2

e)

For events to be mutually exclusive

n(A∩B) = 0 and P(AUB)=P(A)+P(B)

In the given problem

n(A∩B) ≠ 0

So, the events soup delivered to the table and salad delivered to the table are not mutually exclusive

For the events to be independent,

P(A∩B) = P(A) × P(B)

P(A) = 35...

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