Mathematical Methods — Question 17

QCAA 2024, Paper 2 · 3 marks

Q17 · 2024 · Technology-activeComplex familiar3 marks

QUESTION 17 (3 marks)

At a particular orchard, 3% of fruit is bruised during picking. After picking, the fruit is packed into boxes, each containing four pieces of fruit. A grocery shop orders 140 boxes of fruit to sell to their customers. Determine the expected number of boxes that will contain bruised fruit.

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WORKED SOLUTION

QCAA guide · typeset solution

3 marks

ANSWER

Approximately

16

boxes.

Worked solution

Method 1:

P(\text{at least one bruised})=1-P(\text{none bruised})=1-0.97^4=0.11471.

The expected number of such boxes is

140(0.11471)=16.0594\approx16.

Method 2: The expected number with no bruised fruit is

140(0.97^4)=123.9406.

Hence the expected number with at least one bruised fruit is

140-123.9406=16.0594\approx16.

correctly determines the probability of no bruised fruit in a box

[1 mark]

determines the probability of at least one bruised fruit / appropriate complementary expected count

[1 mark]

determines the expected number of boxes

[1 mark]

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Mathematical Methods — Question 17

QUESTION 17 (3 marks)

QCAA guide · typeset solution

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