VCE Maths Methods Basic Probability Mini Test 4
Number of marks: 6
Reading time: 1 minute
Writing time: 9 minutes
Section A – Calculator Allowed
Instructions
• Answer all questions in pencil on your Multiple-Choice Answer Sheet.
• Choose the response that is correct for the question.
• A correct answer scores 1; an incorrect answer scores 0.
• Marks will not be deducted for incorrect answers.
• No marks will be given if more than one answer is completed for any question.
• Unless otherwise indicated, the diagrams in this book are not drawn to scale.
A box contains six red marbles and four blue marbles. Two marbles are drawn from the box, without replacement.
The probability that they are the same colour is
- A. \(\frac{1}{2}\)
- B. \(\frac{28}{45}\)
- C. \(\frac{7}{15}\)
- D. \(\frac{3}{5}\)
- E. \(\frac{1}{3}\)
Let \(A\) and \(B\) be two independent events from a sample space.
If \(\Pr(A) = p\), \(\Pr(B) = p²\) and \(\Pr(A) + \Pr(B) = 1\), then \(\Pr(A' ∪ B)\) is equal to
- A. \(1 - p - p²\)
- B. \(p² - p³\)
- C. \(p - p³\)
- D. \(1 - p + p³\)
- E. \(1 - p - p² + p³\)
In a particular scoring game, there are two boxes of marbles and a player must randomly select one marble from each box. The first box contains four white marbles and two red marbles. The second box contains two white marbles and three red marbles. Each white marble scores \(-2\) points and each red marble scores \(+3\) points. The points obtained from the two marbles randomly selected by a player are added together to obtain a final score.
What is the probability that the final score will equal \(+1\)?
- A. \(\frac{2}{3}\)
- B. \(\frac{1}{5}\)
- C. \(\frac{2}{5}\)
- D. \(\frac{2}{15}\)
- E. \(\frac{8}{15}\)
End of Section A
Section B – No Calculator
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 company produces motors for refrigerators. There are two assembly lines, Line A and Line B. 5% of the motors assembled on Line A are faulty and 8% of the motors assembled on Line B are faulty. In one hour, 40 motors are produced from Line A and 50 motors are produced from Line B. At the end of an hour, one motor is selected at random from all the motors that have been produced during that hour.
a. What is the probability that the selected motor is faulty? Express your answer in the form \(\frac{1}{b}\), where \(b\) is a positive integer. 2 marks
b. The selected motor is found to be faulty. What is the probability that it was assembled on Line A? Express your answer in the form \(\frac{1}{c}\), where \(c\) is a positive integer. 1 mark
End of examination questions
VCE is a registered trademark of the VCAA. The VCAA does not endorse or make any warranties regarding this study resource. Past VCE exams and related content can be accessed directly at www.vcaa.vic.edu.au
