FINISHED! EVERY YEAR 11 RESOURCE IS NOW AVAILABLE.
VCE Methods Probability Application Task 5
Adapted for Year 11. Unit 1 & 2.
Number of marks: 3
Reading time: 1 minute
Writing time: 5 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.
At an airport, luggage is weighed before it is checked in.
A piece of luggage is labelled as heavy if its mass exceeds 23 kg.
a. to b. Not applicable for Year 11.
Use the following information to answer parts c of this question.
Of the travellers flying from the airport
- • 10% do not check in any luggage
- • 40% check in exactly one piece of luggage
- • 50% check in exactly two pieces of luggage
Assume that the mass of each piece of luggage is independent of the number of pieces checked in by each traveller.
Use the value of 0.234 for the probability that a piece of luggage is labelled as heavy.
c. Let \( W \) be the discrete random variable that represents the number of pieces of luggage labelled as heavy checked in by each traveller.
i. Show that \( \Pr(W = 2) = 0.027 \), correct to three decimal places. 1 mark
ii. Complete the table below for the probability distribution \( W \), correct to three decimal places. 2 marks
\[ \begin{array}{|c|c|c|c|} \hline w & 0 & 1 & 2 \\ \hline \Pr(W = w) & & & 0.027 \\ \hline \end{array} \]
End of examination questions
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