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Probability, 2ADV S1 2023 HSC 31

Four Year 12 students want to organise a graduation party. All four students have the same probability, , of being available next Friday. All four students have the same probability, , of being available next Saturday.

It is given that  , and .

Kim is one of the four students.

  1. Is Kim's availability next Friday independent from his availability next Saturday? Justify your answer.  (1 mark)

  2. Show that the probability that Kim is available next Saturday is .  (2 marks)

  3. What is the probability that at least one of the four students is NOT available next Saturday?  (2 marks)

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a.    

b.   

c.   

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a.    

♦♦♦ Mean mark (a) 18%.
b.    
 
 
♦ Mean mark (b) 44%.
   
 
 
 

 

c.    
   
   
♦♦ Mean mark (c) 34%.

Probability, 2ADV S1 2007 MET1 6

Two events, and , from a given event space, are such that    and  .

  1. Calculate    when  .  (1 mark)

  2. Calculate    when and are mutually exclusive events.  (1 mark)

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i.   

♦♦ Mean mark 31%.
MARKER’S COMMENTS: Students who drew a Venn diagram or Karnaugh map were the most successful.

met1-2007-vcaa-q6-answer3

 
 

 

♦♦ Mean mark 23%.
ii.    met1-2007-vcaa-q6-answer4

Probability, 2ADV S1 2015 MET1 8

For events and from a sample space,  and  .

  1.  Calculate  .  (1 mark)

  2.  Calculate  , where denotes the complement of .  (1 mark)

  3.  If events and are independent, calculate  .  (1 mark)

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i.  

 

ii.    met1-2015-vcaa-q8-answer
 
 

 

iii.  

♦♦ Mean mark 28%.
MARKER’S COMMENT: A lack of understanding of independent events was clearly evident.