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Combinatorics, EXT1′ A1 2007 HSC 5a

A bag contains 12 red marbles and 12 yellow marbles. Six marbles are selected at random without replacement.

  1. Calculate the probability that exactly three of the selected marbles are red. Give your answer correct to two decimal places.   (1 mark)

  2. Hence, or otherwise, calculate the probability that more than three of the selected marbles are red. Give your answer correct to two decimal places.   (2 marks)

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Combinatorics, EXT1 A1 2004 HSC 4c

Katie is one of ten members of a social club. Each week one member is selected at random to win a prize.

  1. What is the probability that in the first 7 weeks Katie will win at least 1 prize?  (1 mark)

  2. Show that in the first 20 weeks Katie has a greater chance of winning exactly 2 prizes than of winning exactly 1 prize.  (2 marks)

  3. For how many weeks must Katie participate in the prize drawing so that she has a greater chance of winning exactly 3 prizes than of winning exactly 2 prizes?  (2 marks)

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Combinatorics, EXT1 A1 2004 HSC 2e

A four-person team is to be chosen at random from nine women and seven men.

  1. In how many ways can this team be chosen?  (1 mark)

  2. What is the probability that the team will consist of four women?  (1 mark)

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Combinatorics, EXT1 A1 2006 HSC 3c

Sophie has five coloured blocks: one red, one blue, one green, one yellow and one white. She stacks two, three, four or five blocks on top of one another to form a vertical tower.

  1. How many different towers are there that she could form that are three blocks high?  (1 mark)

  2. How many different towers can she form in total?  (2 marks)

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Combinatorics, EXT1 A1 2015 HSC 14c

Two players and play a series of games against each other to get a prize. In any game, either of the players is equally likely to win.

To begin with, the first player who wins a total of 5 games gets the prize.

  1. Explain why the probability of player getting the prize in exactly 7 games is  .  (1 mark)

  2. Write an expression for the probability of player getting the prize in at most 7 games.  (1 mark)

  3. Suppose now that the prize is given to the first player to win a total of games, where is a positive integer.

     

    By considering the probability that gets the prize, prove that
     

  4. .   (2 marks)

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i.   

♦♦♦ Mean mark 19%.


 

 

ii. 

♦♦♦ Mean mark 23%.

♦♦♦ Mean mark part (iii) 9%.

 

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Combinatorics, EXT1 A1 2011 HSC 2e

Alex’s playlist consists of 40 different songs that can be arranged in any order.  

  1. How many arrangements are there for the 40 songs?    (1 mark)

  2. Alex decides that she wants to play her three favourite songs first, in any order.
  3. How many arrangements of the 40 songs are now possible?   (1 mark)

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