Download 3.3 Homework Assignment 3 - Mr-Kuijpers-Math

Achievement Standard 3.3 Homework Assignment 3
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 wish to draw a probability tree.
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.
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?
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.
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.
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.