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Q. 2.1

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A First Course in Probability
Found in: Page 54
A First Course in Probability

A First Course in Probability

Book edition 9th
Author(s) Sheldon M. Ross
Pages 432 pages
ISBN 9780321794772

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Short Answer

1. A cafeteria offers a three-course meal consisting of an entree, a starch, and a dessert. The possible choices are given in the following table:

CourseChoices
EntreeChicken or roast beef
StarchPasta or rice or potatoes
DessertIce cream or Jello or apple pie or a peach

A person is to choose one course from each category.

(a)How many outcomes are in the sample space?

(b)Let Abe the event that ice cream is chosen. How many outcomes are inA?

(c)Let Bbe the event that chicken is chosen. How many outcomes are inB?

(d)List all the outcomes in the event AB.

(e) LetC be the event that rice is chosen. How many outcomes are in C?

(f)List all the outcomes in the eventABC.

A) 24 .

B)6 .

C) 12 .

D)AB={(Chicken, Pasta, Ice Cream), (Chicken, Rice, Ice cream), (Chicken, Potatoes, Ice Cream)}.

E) 8 .

F)ABC={(Chicken, Rice, Ice Cream)}

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1 Given Information.

A cafeteria offers a three-course meal consisting of an entree, a starch, and a dessert.

Step 2 Explanation.

3Course meal has to be selected i.e1Entree, 1starch, and 1Dessert. For Entrees, we have2 options of Chicken or Roasted Beef. For Starch, we have3 options of Pasta, Rice, or Potatoes.

For dessert, we have 4options Ice cream, Jello, apple pie, or a peach.

Step 3 Part (a) Explanation.

To calculate the no. of outcomes we have to find out the total no. of possible combinations of Entree, Starch, and Dessert. Total No. of ways to select1 Entree from2 Entree=2Cl=2. Total No. of ways to select 1Starch from 3Starch=3Cl=3. Total No. of ways to select1. Dessert from 4Dessert=4Cl=4. Total outcome=(No. of ways to select1 Entree)(No. of ways to select 1Starch) (No. of ways to select 1 Dessert). Total no. of the outcomelocalid="1649313824420" =234=24.

Step 4 Part (b) Explanation.

Total No. of ways to select DessertA=1(Ice cream chosen). To calculate the no. of outcomes in Awe have to find out the total no. of possible combinations of Entree and Starch. Total No. of ways to select 1Entree from 2Entree=2Cl=2. Total No. of ways to select1Starch from3Starch=3Cl=3.

The total outcome inA=( (No. of ways to select Entree)(No. of ways to select Starch)(No. of ways to select Dessert). Total no. of the outcomelocalid="1649313847437" =231=6.

Step 5 Part (c) Explanation.

Total No. of ways to select Entree=1(Chicken chosen). To calculate the no. of outcomes in Bwe have to find out the total no. of possible combinations of Dessert and Starch. Total No. of ways to select 1Dessert from4 Dessert=4Cl=4. Total No. of ways to select1 starch from 3Starch=3Cl=3.

The total outcome inB= (No. of ways to select Entree)(No. of ways to select Starch)(No. of ways to select Dessert). Total no. of outcome=134=12.

Step 6 Part (d) Explanation.

Total No. of ways to select Entree=1(Chicken chosen). Total No. of ways to select Dessert =1(Ice Cream Chosen). To calculate the no. of outcomes in ABwe have to find the ways of choosing Starch. Total No. of ways to select 1 Starch from 3 Starch=3Cl=3.

The total outcome inAB=(No. of ways to select Entree)(No. of ways to select Starch)(No. of ways to select Dessert). Total no. of the outcome= 131= 3. Outcomes are->

localid="1649313866242" AB=(Chicken, Pasta, Ice Cream), (Chicken, Rice, Ice cream), (Chicken, Potatoes, Ice Cream).

Step 7 Part (e) Explanation.

Total No. of ways to select Starch=1(Rice chosen). To calculate the no. of outcomes in Cwe have to find out the total no. of possible combinations of Dessert and Entree. Total No. of ways to select1 Entree from2 Entree=2C1=2. Total No. of ways to select1 Dessert from3 Dessert=4Cl=4.

The total outcome inA=((No. of ways to select Entree)(No. of ways to select Starch)(No. of ways to select Dessert). Total no. of outcome=2 / 4=8.

Step 8 Part (f) Explanation.

Total No. of ways to select Starch= 1(Rice chosen). Total No. of ways to select Entree= 1(Chicken Chosen). Total No. of ways to select Dessert= 1(Ice Cream).

The total outcome in A=(No. of ways to select Entree)(No. of ways to select Starch)(No. of ways to select Dessert). Total no. of outcome= 1l=1. Outcome=(Chicken, Rice, Ice Cream).

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