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Probability, 2ADV S1 2016 HSC 15b

An eight- sided die is marked with numbers  1, 2, … , 8. A game is played by rolling the die until an 8 appears on the uppermost face. At this point the game ends.

  1. Using a tree diagram, or otherwise, explain why the probability of the game ending before the fourth roll is

      

    .  (2 marks)

  2. What is the smallest value of for which the probability of the game ending before the th roll is more than  ?  (3 marks)

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i.  

 

ii. 

♦♦ Mean mark 29%.
ALGEBRA: Note that dividing by reverses the < sign as it is dividing by a negative number.
 

Probability, 2ADV S1 2013 HSC 15d

Pat and Chandra are playing a game. They take turns throwing two dice. The game is won by the first player to throw a double six. Pat starts the game.

  1. Find the probability that Pat wins the game on the first throw.     (1 mark)

  2. What is the probability that Pat wins the game on the first or on the second throw?     (2 marks)

  3. Find the probability that Pat eventually wins the game.     (2 marks)

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i.   

 
 

 

ii.  

 

♦♦ Mean mark 33%
MARKER’S COMMENT: Many students did not account for Chandra having to lose when Pat wins on the 2nd attempt.

 

iii. 

 

♦♦♦ Mean mark 8%!
 COMMENT: Be aware that diminishing probabilities and within the Series and Applications are a natural cross-topic combination.

 

 
 
 

 

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