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2016 VCE Maths Methods Mini Test 6
Adapted for Year 11. Unit 1 & 2.
Number of marks: 4
Reading time: 1 minute
Writing time: 6 minutes
Section B – Calculator Allowed
Instructions
• Answer all questions in the spaces provided.
• Write your responses in English.
• In questions where a numerical answer is required, an exact value must be given unless otherwise specified.
• In questions where more than one mark is available, appropriate working must be shown.
• Unless otherwise indicated, the diagrams in this book are not drawn to scale.
A school has a class set of 22 new laptops kept in a recharging trolley. Provided each laptop is correctly plugged into the trolley after use, its battery recharges.
On a particular day, a class of 22 students uses the laptops. All laptop batteries are fully charged at the start of the lesson. Each student uses and returns exactly one laptop. The probability that a student does not correctly plug their laptop into the trolley at the end of the lesson is 10%. The correctness of any student's plugging-in is independent of any other student's correctness.
a. Determine the probability that at least one of the laptops is not correctly plugged into the trolley at the end of the lesson. Give your answer correct to four decimal places. 2 marks
b. A teacher observes that at least one of the returned laptops is not correctly plugged into the trolley.
Given this, find the probability that fewer than five laptops are not correctly plugged in. Give your answer correct to four decimal places. 2 marks
End of examination questions
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