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Probability, 2ADV S1 2018 HSC 16b

A game involves rolling two six-sided dice, followed by rolling a third six-sided die. To win the game, the number rolled on the third die must lie between the two numbers rolled previously. For example, if the first two dice show 1 and 4, the game can only be won by rolling a 2 or 3 with the third die.

  1. What is the probability that a player has no chance of winning before rolling the third die?   (2 marks)

  2. What is the probability that a player wins the game?   (2 marks)

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♦ Mean mark 40%.
COMMENT: Constructing the full sample space is a critical step here..


 

 
 

 

ii.   

♦♦♦ Mean mark 7%.

 
 
 

Probability, 2ADV S1 2004 HSC 6c

In a game, a turn involves rolling two dice, each with faces marked  0, 1, 2, 3, 4 and 5. The score for each turn is calculated by multiplying the two numbers uppermost on the dice.

  1. What is the probability of scoring zero on the first turn?  (2 marks)

  2. What is the probability of scoring or more on the first turn?  (1 mark)

  3. What is the probability that the sum of the scores in the first two turns is less than 45?  (2 marks)

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MARKER’S COMMENT: Students who drew up the table for the sample space were “overwhelmingly” more successful in all parts of this question.
i.    Probability, 2UA 2004 HSC 6c

 

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Probability, 2ADV S1 2007 HSC 4b

Two ordinary dice are rolled. The score is the sum of the numbers on the top faces.

  1. What is the probability that the score is 10?  (2 marks)

  2. What is the probability that the score is not 10?  (1 mark)

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i. 2UA HSC 2007 4b

 

ii.