• These questions reflect the important skills introduced in this chapter.
• Errors made will indicate areas of weakness.
• Each weakness should be treated by going back to the section listed.
These questions can be used to assess outcomes NS5·1·3 and NS5·3·2.
st e ct sit gaiond
3
1 a What is the probability of choosing a 9 from a list of random digits, (0 to 9)?
b Fifty cards numbered 1 to 50 were shuffled. One of these cards is to be selected at random. What is the probability that the card will be:
i 3? ii less than 11? iii not 3? iv prime?
2 My last 44 scores on our golf course have been entered in this table.
I am about to play another game. What is the experimental probability that my score will be:
a lower than 94? b higher than 93? c higher than 109?
Explain why the experimental probability that my score is higher than 109 is not the real probability.
3 A dice is thrown and a coin is tossed. Show all possible outcomes:
a as a list b as a table c as a tree diagram
4 Four cards marked 6, 7, 8 and 9 are in a hat. One card is drawn out and placed on a table. This is to be the tens digit of a two-digit number.
Another card is then drawn out of the hat and placed beside the first card to complete the number.
a Draw a tree diagram to show the sample space of this experiment.
b How many outcomes are in the sample space?
c If the cards are drawn at random, what is the chance of getting the number 78?
5 This diagram shows the outcomes possible if a spinner showing 1, 2 and 3 is spun and a dice is thrown.
a How many outcomes are in this compound event?
b If the spinner is spun and the dice is thrown, what is the probability that we would get:
i a 2 on the spinner and a 5 on the dice?
ii a total of 7? iii a total of 10 or more?
Section 3:01
3:01
3:02
3:03
3:03 3:04 My score 90–93 94–97 98–101 102–105 106–109
Frequency 3 5 7 20 9
1
2
3
1 2 3 4 5 6 1
1 2 3 4 5 6 2
1 2 3 4 5 6 3 Start
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6 Rachel is choosing the background colour for three consecutive pages of her art assignment. For the first page she must choose either red, blue or green; for the second page, blue or orange; and for the third page, red or blue.
a Draw a tree diagram to show all possible choices.
b If Rachel selects each colour at random, find the probability that at least two of the pages will be blue.
7 This dot diagram shows the types of screwdriver that we manufacture.
The dots show the ones we have in stock. Assume that each size is just as likely to be ordered.
a What is the probability that the next screwdriver ordered is in stock?
b What is the probability that the next one ordered is not in stock?
8 People chose the colour they would prefer in our new range of tennis racquets. The contingency table summarises their preferences. If one of their preferences were chosen at
random, what is the probability that:
a it would be red?
b it would be from a boy?
c it would be from a female?
d it would be from a girl whose preference was blue?
9 The absentee records of the factory workers have been displayed in this frequency table. If one is selected at random, what is the probability that the worker has been absent for:
a 4 days?
Boys Girls Men Women Totals
Gold 15 10 3 6 34
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NEW SIGNPOST MATHEMATICS 10 STAGE 5.1–5.3Chapter 3 | Revision Assignment
1
Presuming that the figures shown in the table are typical of the people in a certain town, what is the probability of a person chosen at random from this town being:
a a blond? b a red-head?
c not a blond?
2 If two dice are rolled, what is the probability that the total will be:
a 8? b 2 or 3?
c a prime number? d 6 or a double?
3 A box contains 10 apples, 8 oranges and 2 lemons. If a piece of fruit is picked at random, what is the chance of getting:
a an orange?
b a lemon?
c an orange or a lemon?
d a banana?
4
A game is played by picking a card at random from a pack of 52 playing cards.
The table shows the results for picking various cards. If Erica picks a card, what is the probability that she will:
a lose money?
b neither win nor lose?
c win money?
d not lose money?
5 Draw a tree diagram to show the possible outcomes when four coins are tossed. Use this to determine the probability of the following outcomes.
a 4 heads b 2 heads, 2 tails c 3 tails, 1 head d at least 2 tails 6 Five books are on a shelf and two are selected. What is the probability that:
a a particular book is included?
b a particular book is not included?
Hint: Draw a tree diagram; let the books be A, B, C, D and E.
nt me gin ass
3A Hair type Number
Brown
10 Of 85 employees in our factory, 35 are married and of these 7 are among the 15 office staff. If one is chosen at random, what is the probability that the employee:
a is married?
b is a married office worker?
c is married but does not work in the office?
d is neither married nor works in the office?
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Chapter 3 | Working Mathematically
1 Of 30 people in our class, 9 can catch left-handed, 24 can catch right-handed and 6 can catch with both their left hands and their right hands.
a How many can catch only with the left hand?
b How many can catch only with the right hand?
c How many cannot catch with one hand?
2 Tina’s investment account had these conditions: ‘4% pa on minimum monthly balance. Interest credited twice yearly.
Open account with $500 or more and maintain a minimum balance of $500.
Deposits of any amount $1 and upwards are then accepted. Funds must be lodged for 30 days and then are available at call (without notice). Minimum withdrawal is
$100 and a cash limit of $500 per day is placed on withdrawals.’
a How often is interest credited to this account?
b How often is interest calculated?
c What is the least amount needed to receive the 4% rate?
d How long must funds be left in the account before they are available?
e What is the minimum amount that can be withdrawn?
3 A cubic block is made up of centimetre cubes, as shown in the diagram. If the entire outside is painted, how many centimetre cubes will have:
a 0 faces painted?
b 1 face painted?
c 2 faces painted?
d 3 faces painted?
e 4 faces painted?
4 How many different pathways, leading from left to right, spell out the word SOLVE?
5 a Complete the table below for n = 2a + 1.
b If a and b are positive integers, are these expressions odd or even?
i 2a ii 4ab
iii 2a + 1 iv 2a + 2 v 2b + 1
c Prove that the product of two odd numbers is always odd. (Hint: Let the odd numbers be 2a + 1 and 2b + 1.)
Probability investigation
1 Theoretical probability 2 Probability and cards
assignme
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NEW SIGNPOST MATHEMATICS 10 STAGE 5.1–5.3aIncludes fatalities of unstated age Source: Federal Office of Road Safety
bIncludes pillion passengers
cIncludes fatalities of unstated road user group
dIncludes fatalities of unstated gender
a What percentage of all fatalities were female?
b What percentage of ‘driver’ fatalities were male?
c What percentage of all fatalities were motorcyclists?
d What percentage of motorcyclist fatalities were male?
e Is it fair to say that females are much safer motorcyclists than males?
Give a reason for your answer.
f The gender of one fatality was ‘unstated’. In which category and age group did this person belong?
g In which age group is the percentage of all female fatalities the lowest?
6 Fatalities by road user category, gender and age, Australia, 2002 0–4 All road usersc
Males
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