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Selwyn College
Level 3 Statistics and Modelling
90643 Solve straightforward problems involving probability.
Credits: Four
Answer ALL questions in the spaces provided in this booklet.
You should show ALL working.
Check that this booklet has pages 2–8 in the correct order and that none of these
pages is blank.
YOU MUST HAND THIS BOOKLET TO THE SUPERVISOR AT THE END OF
THE EXAMINATION.
For Assessor’s use only
Achievement Criteria
Achievement
Solve straight forward
problems involving
probability.
Achievement with Merit
Solve probability
problems.
Overall level of Performance
Achievement with
Excellence
Apply probability theory.
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You are advised to spend 40 minutes answering the questions in this booklet.
Show ALL working
Question One
A biased coin has a
3
chance of landing Heads (H) up.
5
Are you more likely to get one Head or two Heads in three tosses of the coin? Justify
your answer.
(You may want to draw a probability tree below)
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Question Two
A very large department store sells two types of plasma television. Type A is available
70% of the time and type B is available 85% of the time. Both types are available 65% of
the time.
A customer wishes to purchase a new plasma television.
a)
What is the probability that the customer will find at least one type of plasma is
available from the department store?
b) Are the events “Type A is available” and “Type B is available” independent events?
Justify your answer.
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Question Three
The supplier to the department store imports three brands of DVD players.
45% of the DVD players are Brand X, 25% are Brand Y and 30% are Brand Z. It is
known that some of the DVD players develop a fault while under warranty. Past
experience has shown that 5% of Brand X, 20% of Brand Y and 8% of Brand Z develop a
fault while under warranty.
a)
Find the probability that a randomly chosen DVD player will develop a fault while
under warranty.
b)
Given that a DVD player did develop a fault while under warranty, what is the
probability that it was a Brand X DVD player?
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Question Four
The department store is offering an incentive for customers to buy a new DVD player.
The customer is given two fair dice to toss. If the sum of the numbers that turn up is 11
or more the customer is given $100 discount on the price of the DVD player. If the sum
of the numbers is less than 5 then a discount of $50 is given.
If 20 customers buy DVDs during this promotion, find the expected discount on the
DVDs.
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Question Five
The movie watching habits of a large number of married couples in the city were
analysed. It was found that 15% of husbands watch movies and, if the husband watches a
movie then there is a 75% chance the wife also watches the movie.
Use this information to calculate the probability that the husband and wife both watch the
movie
Question Six
The department store wants to employ five more sales assistants. Nine females and
twelve males apply for the five positions. Calculate the probability that more females
than males are appointed to the positions.
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Question Seven
Another large department store has found that 10% of all DVD players purchased in any
given year are returned. The manager of the department store is concerned about the
number of DVD players which are returned but are not faulty. Data available indicates
that 8% of all DVDs are faulty. It is found that 25% of the returned DVDs are in fact not
faulty.
Calculate the probability that a DVD player that is not faulty is returned.
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