0. Rachel is playing a game of chance in which she tosses a dart into a rotating dartboard with 8 equal-sized slices numbered 1 through 8. The dart lands on a numbered slice at random. This game is this: Rachel tosses the dart once. She wins $1 if the dart lands in slice 1, $2 if the dart lands in slice 2, $5 if the dart lands in slice 3 , and $8 if the dart lands in slice 4. She loses $2.50 if the dart lands in slices 5, 6, 7, or 8. (a) Find the expected value of playing the game.   dollars   (b) What can Rachel expect in the long run, after playing the game many times?     Rachel can expect to gain money.   She can expect to win (   ) dollars per toss.     Rachel can expect to lose money.

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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10. Rachel is playing a game of chance in which she tosses a dart into a rotating dartboard with 8 equal-sized slices numbered 1 through 8. The dart lands on a numbered slice at random. This game is this: Rachel tosses the dart once. She wins $1 if the dart lands in slice 1, $2 if the dart lands in slice 2, $5 if the dart lands in slice 3 , and $8 if the dart lands in slice 4. She loses $2.50 if the dart lands in slices 5, 6, 7, or 8.

(a) Find the expected value of playing the game.
  dollars
 
(b) What can Rachel expect in the long run, after playing the game many times?
 
 

Rachel can expect to gain money.

  She can expect to win (   ) dollars per toss.
 
 

Rachel can expect to lose money.

  She can expect to lose (  )  dollars per toss.
 
 

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

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