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Q. 2.1

Expert-verifiedFound in: Page 54

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:

Course | Choices |

Entree | Chicken or roast beef |

Starch | Pasta or rice or potatoes |

Dessert | Ice cream or Jello or apple pie or a peach |

A 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$ABC.$

$A)24.$

$B)6.$

$C)12.$

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

$E)8.$

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

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

$3$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.

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" $=234=24$.

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$\mathrm{A}=($ (No. of ways to select Entree)(No. of ways to select Starch)(No. of ways to select Dessert). Total no. of the outcomelocalid="1649313847437" $=231=6$.

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=$134=12$.

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

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$\mathrm{A}=($(No. of ways to select Entree)(No. of ways to select Starch)(No. of ways to select Dessert). Total no. of outcome=$2/4=8$.

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 $\mathrm{A}=($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).

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