### Select your language

Suggested languages for you:

Americas

Europe

Q. 2.1

Expert-verified
Found in: Page 54

### A First Course in Probability

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

# 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:CourseChoicesEntreeChicken or roast beefStarchPasta or rice or potatoesDessertIce cream or Jello or apple pie or a peachA person is to choose one course from each category.$\left(a\right)$How many outcomes are in the sample space?$\left(b\right)$Let $A$be the event that ice cream is chosen. How many outcomes are in$A?$$\left(c\right)$Let $B$be the event that chicken is chosen. How many outcomes are in$B?$$\left(d\right)$List all the outcomes in the event$AB.$$\left(e\right)$Let$C$ be the event that rice is chosen. How many outcomes are in$C?$$\left(f\right)$List all the outcomes in the event$ABC.$

$A\right)24.$

$B\right)6.$

$C\right)12.$

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

$E\right)8.$

$F\right)$$ABC=\left\{\left($Chicken, Rice, Ice Cream)}

See the step by step solution

## Step 1 Given Information.

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

## Step 2 Explanation.

$3$Course meal has to be selected i.e$1$Entree, $1$starch, and $1$Dessert. For Entrees, we have$2$ options of Chicken or Roasted Beef. For Starch, we have$3$ options of Pasta, Rice, or Potatoes.

For dessert, we have $4$options 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 select$1$ Entree from$2$ Entree=$2\mathrm{Cl}=2$. Total No. of ways to select $1$Starch from $3$Starch$=3\mathrm{Cl}=3$. Total No. of ways to select$1$. Dessert from $4$Dessert$=4\mathrm{Cl}=4$. Total outcome=(No. of ways to select$1$ Entree)(No. of ways to select $1$Starch) (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 Dessert$A=1$(Ice cream chosen). To calculate the no. of outcomes in $A$we have to find out the total no. of possible combinations of Entree and Starch. Total No. of ways to select $1$Entree from $2$Entree$=2\mathrm{Cl}=2$. Total No. of ways to select$1$Starch from$3\mathrm{Starch}=3\mathrm{Cl}=3$.

The total outcome in$\mathrm{A}=\left($ (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 $B$we have to find out the total no. of possible combinations of Dessert and Starch. Total No. of ways to select $1$Dessert from$4$ Dessert=$4\mathrm{Cl}=4$. Total No. of ways to select$1$ starch from $3$Starch$=3\mathrm{Cl}=3$.

The total outcome in$B=$ (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 $AB$we have to find the ways of choosing Starch. Total No. of ways to select 1 Starch from 3 Starch$=3\mathrm{Cl}=3$.

The total outcome in$AB=$(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" $AB=\left($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 $C$we have to find out the total no. of possible combinations of Dessert and Entree. Total No. of ways to select$1$ Entree from$2$ Entree=$2C1=2$. Total No. of ways to select$1$ Dessert from$3$ Dessert=$4Cl=4$.

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