FINISHED! EVERY YEAR 11 RESOURCE IS NOW AVAILABLE.
VCE Methods Probability Application Task 4
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.
Doctors are studying the resting heart rate of adults in two neighbouring towns: Mathsland and Statsville. Resting heart rate is measured in beats per minute (bpm).
a. No applicable for Year 11 students.
The doctors consider a person to have a slow heart rate if the person's resting heart rate is less than 60 bpm. The probability that a randomly chosen Mathsland adult has a slow heart rate is 0.1587.
It is known that 29% of Mathsland adults play sport regularly.
It is also known that 9% of Mathsland adults play sport regularly and have a slow heart rate.
Let \(S\) be the event that a randomly selected Mathsland adult plays sport regularly and let \(H\) be the event that a randomly selected Mathsland adult has a slow heart rate.
b.
i. Find \(\Pr(H|S)\), correct to three decimal places. 1 mark
ii. Are the events \(H\) and \(S\) independent? Justify your answer. 1 mark
c.
i. Find the probability that a random sample of 16 Mathsland adults will contain exactly one person with a slow heart rate. Give your answer correct to three decimal places. 2 marks
End of examination questions
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