smc-2736-30-Venn Diagrams

Probability, MET1 2020 VCAA 2

A car manufacturer is reviewing the performance of its car model X. It is known that at any given six-month service, the probability of model X requiring an oil change is , the probability of model X requiring an air filter change is and the probability of model X requiring both is .

State the probability that at any given six-month service model X will require an air filter change without an oil change. (1 mark)

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The car manufacturer is developing a new model. The production goals are that the probability of model Y requiring an oil change at any given six-month service will be , the probability of model Y requiring an air filter change will be and the probability of model Y requiring both will be , where .
Determine in terms of if the probability of model Y requiring an air filter change without an oil change at any given six-month service is 0.05. (2 marks)

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Probability, MET1 2017 VCAA 8

For events and from a sample space, and . Let .

Find in terms of . (1 mark)

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Find in terms of . (2 marks)

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Given that , state the largest possible interval for . (2 marks)

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a.

♦ Mean mark 40%.
MARKER’S COMMENT: The most successful answers used a Venn diagram or table.

♦ Mean mark 37%.

Probability, MET2 2011 VCAA 21 MC

For two events, and , .

and will be independent events exactly when

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♦♦♦ Mean mark 15%.

Probability, MET1 2007 VCAA 6

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

Calculate when . (1 mark)

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

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

♦♦ Mean mark (b) 23%.

Probability, MET1 2011 VCAA 8

Two events, and , are such that and

If denotes the compliment of , calculate when

(2 marks)

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and are mutually exclusive. (1 mark)

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Probability, MET1 2015 VCAA 8

For events and from a sample space, and .

Calculate . (1 mark)

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

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

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