Kala has a bag with 8 balls numbered 1 through 8 . She is playing a game of chance. This game is this: Kala chooses one ball from the bag at random. She wins $1 if the number 1 is selected, $2 if the number 2 is selected, $5 if the number 3 is selected, $6 if the number 4 is selected, $8 if the number 5 is selected, and $10 if the number 6 is selected. She loses $14 if 7 or 8 is selected.   (a) Find the expected value of playing the game.   dollars   (b) What can Kala expect in the long run, after playing the game many times? (She replaces the ball in the bag each time.)       Kala can expect to gain money.   Shecanexpecttowindollarsperselection.       Kala can expect to lose money.   Shecanexpecttolosedollarsperselection.       Kala can expect to break even (neither gain nor lose money).

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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Kala has a bag with

8

balls numbered

1

through

8

. She is playing a game of chance.

This game is this: Kala chooses one ball from the bag at random. She wins

$1

if the number

1

is selected,

$2

if the number

2

is selected,

$5

if the number

3

is selected,

$6

if the number

4

is selected,

$8

if the number

5

is selected, and

$10

if the number

6

is selected. She loses

$14

if

7

or

8

is selected.

 

(a) Find the expected value of playing the game.
 

dollars

 
(b) What can Kala expect in the long run, after playing the game many times?
(She replaces the ball in the bag each time.)
 
 

 

Kala can expect to gain money.
 

Shecanexpecttowindollarsperselection.

 
 

 

Kala can expect to lose money.
 

Shecanexpecttolosedollarsperselection.

 
 

 

Kala can expect to break even (neither gain nor lose money).
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