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Chapter 5 Problem Post

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Chapter 5 Problem Post
1) Question 4, Page 280
a)
The two outcomes are that the player wins $25 or loses $10. There 14 marbles when the player first
draws and 13 marbles on the second draw. The probability the player wins is:




Therefore:


   

 



   


  



 
 
b)
The expected value to the player is the negative of the expected value of the game to the animal
shelter. Therefore, the expected value of the game to the shelter 




Using this:
   
  





 
  
2) Question 8, page 281
In this scenario, we are pulling batteries and throwing them out if it is defective and keeping it if it’s
one of the two new batteries. This is similar to sampling without replacement and the appropriate
distribution would be the hypergeometric distribution where we have a population (N) of 8, 2
“defects” (M) and we want to find 2 (x) “defects” out of a sample of 4 (n). (The normal terminology is
a defect but, in this scenario, it refers to the new batteries). Therefore:
 
  

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Chapter 5 Problem Post 1) Question 4, Page 280 a) The two outcomes are that the player wins $25 or loses $10. There 14 marbles when the player first draws and 13 marbles on the second draw. The probability the player wins is: 6 5 15 × = 14 13 91 Therefore: 𝑡ℎ𝑒 𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑔𝑎𝑚𝑒 = 𝑃(𝑤𝑖𝑛𝑛𝑖𝑛𝑔) × 𝑤𝑖𝑛𝑛𝑖𝑛𝑔𝑠 + 𝑃(𝑙𝑜𝑠𝑖𝑛𝑔) × 𝑙𝑜𝑠𝑒𝑠 15 15 = × 25 + (1 − ) × −10 91 91 55 =− 13 = −4.230769231 … ≈ −$4.23 b) The expected value ...
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