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Probability, STD2 S2 2018 HSC 9 MC

An experiment has three distinct outcomes, A, B and C.

Outcome A occurs 50% of the time. Outcome B occurs 23% of the time.

What is the expected number of times outcome C would occur if the experiment is conducted 500 times?

  1. 115
  2. 135
  3. 250
  4. 365
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`B`

Show Worked Solution

`text(Expectation of outcome)\ C`

`= 1-0.5-0.23= 0.27`
 

`:.\ text(Expected times)\ C\ text(occurs)`

`= 0.27 xx 500= 135`

`=> B`

Probability, STD2 S2 2006 HSC 1 MC

The probability of an event occurring is `9/10.`

Which statement best describes the probability of this event occurring?

  1. The event is likely to occur.
  2. The event is certain to occur.
  3. The event is unlikely to occur.
  4. The event has an even chance of occurring.
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`A`

Show Worked Solution

`text(The event is highly likely to occur but not certain.)`

`=>  A`

Probability, STD2 S2 2005 HSC 23a

There are 100 tickets sold in a raffle. Justine sold all 100 tickets to five of her friends. The number of tickets she sold to each friend is shown in the table.
 

  1. Justine claims that each of her friends is equally likely to win first prize.

     

    Give a reason why Justine’s statement is NOT correct.   (1 mark)

  2. What is the probability that first prize is NOT won by Khalid or Herman?   (2 marks)

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a.    `text(The claim is incorrect because each of her friends)`

`text(bought a different number of tickets and therefore)`

`text(their chances of winning are different.)`

b.    `69/100`

Show Worked Solution

a.    `text(The claim is incorrect because each of her friends bought)`

`text(a different number of tickets and therefore their chances of)`

`text(winning are different.)`

 

b.    `text(Number of tickets not sold to K or H)= 45 + 10 + 14= 69` 

`:.\ text(Probability 1st prize NOT won by K or H)= 69/100`

Probability, STD2 S2 2005 HSC 3 MC

Four radio stations reported the probability of rain as shown in the table.
 

Which radio station reported the highest probability of rain?

  1. `text(2AT)`
  2. `text(2BW)`
  3. `text(2CZ)`
  4. `text(2DL)`
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`D`

Show Worked Solution

`text(Converting all probabilities to decimals)`

`2AT` `= 0.53`
`2BW` `= 0.17`
`2CZ` `= 0.52`
`2DL` `= 0.60`

  
`=> D`

Probability, STD2 S2 2004 HSC 1 MC

Which fraction is equal to a probability of `text(25%)`?

  1. `1/25`
  2. `1/4`
  3. `1/3`
  4. `1/2`
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`B`

Show Worked Solution

`P=25/100=1/4`

`=> B`

Probability, STD2 S2 2007 HSC 25a

Give an example of an event that has a probability of exactly  `3/4`.   (1 mark)

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`text(Choosing a red ball out of a bag that)`

`text(contains 3 red balls and 1 green ball.)`

`text{(An infinite amount of examples are}`

`text{possible)}`

Show Worked Solution

`text(Choosing a red ball out of a bag that contains)`

`text(3 red balls and 1 green ball.)`

`text{(An infinite amount of examples are}`

`text{possible)}`

Probability, STD2 S2 2011 HSC 15 MC

An unbiased coin is tossed 10 times.

A tail is obtained on each of the first 9 tosses.

What is the probability that a tail is obtained on the 10th toss?

  1. `1/2^10`
  2. `1/2`
  3. `1/10`
  4. `9/10`
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`B`

Show Worked Solution

`text(Each toss is an independent event and has an even chance)`

`text(of being a head or tail.)`

`=> B`

Probability, STD2 S2 2009 HSC 1 MC

A newspaper states: ‘It will most probably rain tomorrow.’

Which of the following best represents the probability of an event that will most probably occur?   

  1. `33 1/3 text(%)` 
  2.  `text(50%)` 
  3. `text(80%)` 
  4. `text(100%)` 
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`C`

Show Worked Solution

`text(Probably) =>\ text(likelihood > 50%)`

`text(However 100% = certainty)`

`:.\ text(80% is the answer)`

`=> C`

Probability, STD2 S2 2011 HSC 2 MC

Which of the following could be the probability of an event occurring?

  1. `1` 
  2. `6/5` 
  3. `1.27` 
  4. `text(145%)` 
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`A`

Show Worked Solution

`text(Probabilities must lie between 0 and 1 inclusive.)`

`=>A`