In the Venn diagram below, shade in the area that represents
`C \cup (B \cap A^{′})` (2 marks)
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Aussie Maths & Science Teachers: Save your time with SmarterEd
In the Venn diagram below, shade in the area that represents
`C \cup (B \cap A^{′})` (2 marks)
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In the Venn diagram below, shade in the area that represents
`(A \cap B) \cup (B \cap C) \cup (A \cap C)` (2 marks)
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In the Venn diagram below, shade in the area that represents
`(A \cap B \cap C) \cup (A \cap C^{′})` (2 marks)
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Students studying vocational education courses were surveyed about their living arrangements.
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i. `text{Number of males living with parents = 155}`
`text{Total students surveyed = 505}`
`P\text{(male and living with parents)}` | `=155/505` | |
`=0.3069…` | ||
`=31\text{% (nearest %)}` |
ii. `text{Number of females = 228}`
`text{Females not living with parents = 182}`
`P\text{(selected female not living with parents)} = 182/228 = 91/114`
A group of coalminers were surveyed about what registered vehicles they own.
They were surveyed on whether they own a car, a motorbike, both or neither and the results were recorded in the Venn diagram below.
Record this information in the partially completed 2-way table below. (2 marks)
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\begin{array} {|l|c|c|}
\hline
\rule{0pt}{2.5ex} &\ \ \ \text{Car}\ \ \ \rule[-1ex]{0pt}{0pt} & \text{No Car}\\
\hline
\rule{0pt}{2.5ex}\text{Motorbike}\rule[-1ex]{0pt}{0pt} & 7 & 8 \\
\hline
\rule{0pt}{2.5ex}\text{No Motorbike}\rule[-1ex]{0pt}{0pt} & 29 & 6 \\
\hline
\end{array}
\begin{array} {|l|c|c|}
\hline
\rule{0pt}{2.5ex} &\ \ \ \text{Car}\ \ \ \rule[-1ex]{0pt}{0pt} & \text{No Car}\\
\hline
\rule{0pt}{2.5ex}\text{Motorbike}\rule[-1ex]{0pt}{0pt} & 7 & 8 \\
\hline
\rule{0pt}{2.5ex}\text{No Motorbike}\rule[-1ex]{0pt}{0pt} & 29 & 6 \\
\hline
\end{array}
A group of 20 museum visitors were surveyed about what languages they could speak fluently.
They were surveyed on whether they could speak English or French and the results were recorded in the Venn diagram below.
Record this information in the partially completed 2-way table below. (2 marks)
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\begin{array} {|l|c|c|}
\hline
\rule{0pt}{2.5ex} & \text{English}\rule[-1ex]{0pt}{0pt} & \text{No English}\\
\hline
\rule{0pt}{2.5ex}\text{French}\rule[-1ex]{0pt}{0pt} & 5 & 3 \\
\hline
\rule{0pt}{2.5ex}\text{No French}\rule[-1ex]{0pt}{0pt} & 8 & 4 \\
\hline
\end{array}
\begin{array} {|l|c|c|}
\hline
\rule{0pt}{2.5ex} & \text{English}\rule[-1ex]{0pt}{0pt} & \text{No English}\\
\hline
\rule{0pt}{2.5ex}\text{French}\rule[-1ex]{0pt}{0pt} & 5 & 3 \\
\hline
\rule{0pt}{2.5ex}\text{No French}\rule[-1ex]{0pt}{0pt} & 8 & 4 \\
\hline
\end{array}
A class of 30 students were surveyed about their pets. They were asked whether they owned a dog, cat, both or neither and the results were recorded in the Venn diagram below.
Record this information in the partially completed 2-way table below. (2 marks)
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\begin{array} {|l|c|c|}
\hline
\rule{0pt}{2.5ex} &\ \ \ \text{Dog}\ \ \ \rule[-1ex]{0pt}{0pt} & \text{No Dog}\\
\hline
\rule{0pt}{2.5ex}\text{Cat}\rule[-1ex]{0pt}{0pt} & 3 & 7 \\
\hline
\rule{0pt}{2.5ex}\text{No Cat}\rule[-1ex]{0pt}{0pt} & 12 & 8\\
\hline
\end{array}
\begin{array} {|l|c|c|}
\hline
\rule{0pt}{2.5ex} &\ \ \ \text{Dog}\ \ \ \rule[-1ex]{0pt}{0pt} & \text{No Dog}\\
\hline
\rule{0pt}{2.5ex}\text{Cat}\rule[-1ex]{0pt}{0pt} & 3 & 7 \\
\hline
\rule{0pt}{2.5ex}\text{No Cat}\rule[-1ex]{0pt}{0pt} & 12 & 8\\
\hline
\end{array}
In the Venn diagram below, shade in the area that represents
`A \cap B \cap C` (2 marks)
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In the Venn diagram below, shade in the area that represents
`B^c \cap C^c` (2 marks)
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In the Venn diagram below, shade in the area that represents
`(A \cap B) \cup C` (2 marks)
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Some men and women were surveyed at a football game. They were asked which team they supported. The results are shown in the two-way table.
\begin{array} {|l|c|c|c|}
\hline
\rule{0pt}{2.5ex} &\ \textit{Team A }\ \rule[-1ex]{0pt}{0pt} &\ \textit{Team B}\ \ &\ \textit{Totals}\ \ \\
\hline
\rule{0pt}{2.5ex}\text{Men}\rule[-1ex]{0pt}{0pt} & 125 & 100 & 225 \\
\hline
\rule{0pt}{2.5ex}\text{Women}\rule[-1ex]{0pt}{0pt} & 75 & 90 & 165 \\
\hline
\rule{0pt}{2.5ex}\text{Totals}\rule[-1ex]{0pt}{0pt} & 200 & 190 & 390 \\
\hline
\end{array}
A man was chosen at random. What is the probability that he supports Team B, correct to the nearest percent? (2 marks)
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`44%`
`text{Total number of men}\ = 225`
`text{Number of men who support Team B}\ = 100`
`P(\text{chosen man supports Team B})`
`=100/225`
`=4/9`
`=44%\ \text{(nearest %)}`
The subject choices in science at a high school are physics, chemistry and biology.
This Venn diagram shows the number of students who are studying each of the subjects.
A student studying Biology is chosen a random.
What is the probability that the student also studies Chemistry? (2 marks)
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`7/40`
`text(Students studying Biology)\ = 4 + 2 + 12 + 62 = 80`
`text(Students studying Biology and Chemistry)\ = 2 + 12 = 14`
`:. P\text{(chosen student studies Chemistry)}`
`= 14/80`
`=7/40`
The subject choices in science at a high school are physics, chemistry and biology.
This Venn diagram shows the number of students who are studying each of the subjects.
How many of these students are studying at least two of these science subjects?
`C`
`text(Any students in overlapping circles study 2 or 3)`
`text(of the science subjects.)`
`:.\ text(Number of students)\ = 8 + 12 + 4 + 2 = 26`
`=>C`
Zilda took a survey of eighteen year olds, asking if they work, go to school, do both or do neither.
The Venn diagram shows the results.
What is the probability that a person randomly selected from the group goes to school and works, rounded to three decimal places? (2 marks)
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`0.067`
`P\ text{(go to school and works)}`
`= 3/(19+3+16+7)`
`= 3/45`
`= 0.067`
A country school surveyed 120 of its students about the type of animals they have at home.
The results are recorded in the Venn diagram below, although the number of students who only own horses is missing.
If one of the students is selected at random, what is the probability that the student does not own a goat?
`C`
`text(Number of students who do not own a goat)`
`= 120-(9 + 7 + 4 + 20)`
`= 120-40`
`= 80`
`:.\ text(Probability) = 80/120`
`=>C`
The table below shows all the people at Angus' birthday party.
What fraction of the children at the party are female?
`A`
`text(Fraction of the children that are female)`
`= text(Female Children) / text(Total Children)`
`=20/60`
`=>A`
A group of 125 people were asked if they wear a watch or not.
This table shows the results.
A man was selected at random.
What is the exact probability that he wears a watch? (2 marks)
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`5/12`
`P(text(man chosen wears watch))`
`= text(number of men wearing watch)/text(total men)`
`= 25/60`
`= 5/12`
On a tray there are 12 hard‑centred chocolates `(H)` and 8 soft‑centred chocolates `(S)`. Two chocolates are selected at random. A partially completed probability tree is shown.
What is the probability of selecting at least one soft-centred chocolate? (3 marks)
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`62/95`
`P(text{at least one}\ S)`
`= 1-P(HH)`
`= 1-(12/20 xx 11/19)`
`= 1-33/95`
`= 62/95`
A game consists of two tokens being drawn at random from a barrel containing 20 tokens. There are 17 red tokens and 3 black tokens. The player keeps the two tokens drawn.
i. |
ii. `P(text(at least one red))`
`= 1-P(BB)`
`= 1-3/20 xx 2/19`
`= 187/190`
Beib owns three white and five blue T-shirts. He chooses a T-shirt at random for himself and puts it on. He then chooses another T-shirt at random, from the remaining T-shirts, and gives it to his brother.
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i. `P(B)= (text(number of blue T-shirts))/(text(total number of T-shirts)) = 5/8`
ii.
iii. `Ptext((same colour))`
`= P(text(WW)) + P(text(BB))`
`= 3/8 xx 2/7 + 5/8 xx 4/7`
`= 6/56 + 20/56`
`= 13/28`
Two dice are rolled. What is the probability that only one of the dice shows a three? (2 marks)
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`5/18`
`text{Each dice roll is an independent event.}`
`P(3) = 1/6, \ P\text{(not 3)} = 1-1/6=5/6`
`text{P (Only one 3)}`
`= P text{(3, not 3)} + P text{(not 3, 3)}`
`= 1/6 xx 5/6 + 5/6 xx 1/6`
`= 10/36`
`= 5/18`
Tay-Tay has 2 bags of apples.
Bag A contains 4 red apples and 3 green apples.
Bag B contains 3 red apples and 1 green apple.
Tay-Tay chooses one of the bags randomly and with her eyes closed, takes one of the apples.
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i.
ii. `37/56`
i.
ii. | `Ptext{(red)}` | `=1/2 xx 4/7 + 1/2 xx 3/4` |
`=37/56` |
Each time she throws a dart, the probability that Gaga hits the dartboard is `4/7`.
She throws two darts, one after the other.
What is the probability that she misses the dartboard with both darts? (2 marks)
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`9/49`
`P text{(hits)} = 4/7\ \ =>\ \ P\text{(misses)} = 1-4/7=3/7`
`P text{(misses twice)}` | `= 3/7 xx 3/7` |
`= 9/49` |
Jon spins each pointer 50 times.
Each time he added the numbers that the pointers landed on.
His results are shown below.
\begin{array} {|c|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex}\textbf{Sum of numbers}\rule[-1ex]{0pt}{0pt} & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 & \textbf{Total}\\
\hline
\rule{0pt}{2.5ex}\textbf{Number of spins}\rule[-1ex]{0pt}{0pt} & 1 & 2 & 3 & 6 & 8 & 9 & 7 & 5 & 4 & 4 & 1 & \textbf{50} \\
\hline
\end{array}
What percentage of the spins resulted in a sum of 9? (2 marks)
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`text(10%)`
`text(Percentage)` | `= text(number of 9’s)/text(number of spins) xx 100` |
`=5/50 xx 100` | |
`=10 text(%)` |
Two fair 20 cent coins are tossed at the same time.
What is the probability that both coins will show heads? (2 marks)
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`1/4`
`text(Possible outcomes are:)`
`text(HH, HT, TH, TT.)`
`:. P text{(HH)} = 1/4`
Brandi spins the arrow on two identical spinners.
The arrow on each spinner is equally likely to land on 1, 2 or 3.
If Brandi adds up the two results, which total is she least likely to get?
`A`
`text{2 can only result from (1, 1).}`
`text(All other totals can have more than 1 combination producing them.)`
`=>A`
Bromley rolls two standard dice at the same time and adds up the total.
An incomplete table of the possible outcomes is below.
\begin{array} {|c|c|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex}\textbf{Face} \rule[-1ex]{0pt}{0pt} & \textbf{1} & \textbf{2} & \textbf{3} & \textbf{4} & \textbf{5} & \textbf{6}\\
\hline
\rule{0pt}{2.5ex}\textbf{1}\rule[-1ex]{0pt}{0pt} & 2 & 3 & 4 & 5 & 6 & 7 \\
\hline
\rule{0pt}{2.5ex}\textbf{2}\rule[-1ex]{0pt}{0pt} & 3 & 4 & 5 & & & 8 \\
\hline
\rule{0pt}{2.5ex}\textbf{3}\rule[-1ex]{0pt}{0pt} & 4 & 5 & 6 & & & 9 \\
\hline
\rule{0pt}{2.5ex}\textbf{4}\rule[-1ex]{0pt}{0pt} & 5 & & 7 & 8 & 9 & 10 \\
\hline
\rule{0pt}{2.5ex}\textbf{5}\rule[-1ex]{0pt}{0pt} & 6 & & 8 & & 10 & 11 \\
\hline
\rule{0pt}{2.5ex}\textbf{6}\rule[-1ex]{0pt}{0pt} & 7 & 8 & 9 & 10 & 11 & 12 \\
\hline
\end{array}
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i.
\begin{array} {|c|c|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex}\textbf{Face} \rule[-1ex]{0pt}{0pt} & \textbf{1} & \textbf{2} & \textbf{3} & \textbf{4} & \textbf{5} & \textbf{6}\\
\hline
\rule{0pt}{2.5ex}\textbf{1}\rule[-1ex]{0pt}{0pt} & 2 & 3 & 4 & 5 & 6 & 7 \\
\hline
\rule{0pt}{2.5ex}\textbf{2}\rule[-1ex]{0pt}{0pt} & 3 & 4 & 5 & \colorbox{lightblue}{6} & \colorbox{lightblue}{7} & 8 \\
\hline
\rule{0pt}{2.5ex}\textbf{3}\rule[-1ex]{0pt}{0pt} & 4 & 5 & 6 & \colorbox{lightblue}{7} & \colorbox{lightblue}{8} & 9 \\
\hline
\rule{0pt}{2.5ex}\textbf{4}\rule[-1ex]{0pt}{0pt} & 5 & \colorbox{lightblue}{6} & 7 & 8 & 9 & 10 \\
\hline
\rule{0pt}{2.5ex}\textbf{5}\rule[-1ex]{0pt}{0pt} & 6 & \colorbox{lightblue}{7} & 8 & \colorbox{lightblue}{9} & 10 & 11 \\
\hline
\rule{0pt}{2.5ex}\textbf{6}\rule[-1ex]{0pt}{0pt} & 7 & 8 & 9 & 10 & 11 & 12 \\
\hline
\end{array}
ii. `7`
i.
\begin{array} {|c|c|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex}\textbf{Face} \rule[-1ex]{0pt}{0pt} & \textbf{1} & \textbf{2} & \textbf{3} & \textbf{4} & \textbf{5} & \textbf{6}\\
\hline
\rule{0pt}{2.5ex}\textbf{1}\rule[-1ex]{0pt}{0pt} & 2 & 3 & 4 & 5 & 6 & 7 \\
\hline
\rule{0pt}{2.5ex}\textbf{2}\rule[-1ex]{0pt}{0pt} & 3 & 4 & 5 & \colorbox{lightblue}{6} & \colorbox{lightblue}{7} & 8 \\
\hline
\rule{0pt}{2.5ex}\textbf{3}\rule[-1ex]{0pt}{0pt} & 4 & 5 & 6 & \colorbox{lightblue}{7} & \colorbox{lightblue}{8} & 9 \\
\hline
\rule{0pt}{2.5ex}\textbf{4}\rule[-1ex]{0pt}{0pt} & 5 & \colorbox{lightblue}{6} & 7 & 8 & 9 & 10 \\
\hline
\rule{0pt}{2.5ex}\textbf{5}\rule[-1ex]{0pt}{0pt} & 6 & \colorbox{lightblue}{7} & 8 & \colorbox{lightblue}{9} & 10 & 11 \\
\hline
\rule{0pt}{2.5ex}\textbf{6}\rule[-1ex]{0pt}{0pt} & 7 & 8 & 9 & 10 & 11 & 12 \\
\hline
\end{array}
ii. `text{The most frequent total = 7 (6 times)}`
`:.\ text{7 is the most likely to be rolled.}`
Two standard dice are rolled at the same time and the two numbers are added up.
Which total is most likely?
`D`
`text(A total of 6 is most likely.)`
`text{Note that a 6 can occur in the following ways:}`
`(5,1), (1,5), (4,2), (2,4) and (3,3)`
`text(No other option given has as many combinations.)`
Peter has a bag of marbles. 75% of his marbles are blue.
Peter takes a green marble from his bag and loses it in a game.
If he takes another marble from the bag without looking, what are the chances it is blue?
`C`
`text{Taking marbles two times without replacement → dependent events.}`
`text(When taking the second marble, there will be greater than 75% chance)`
`text(of choosing blue because there are the same amount of blue marbles)`
`text(to be chosen but 1 less marble of another colour.)`
`=>C`
Arun flips an unbiased coin 200 times.
Which result is most likely?
`B`
`text{Each toss is an independent event with 50% chance for both heads and tails}.`
`text{The expected result after 200 tosses is 100 tails, 100 heads.}`
`:.\ text{The most likely result = 98 tails (closest to 100)}`
`=> B`
A representative soccer team is chosen from 30 players who play for two clubs, Portland and Lithgow.
10 players from Portland and 20 players from Lithgow are playing in the trials, and 7 players from Portland and 8 from Lithgow are selected in the representative team.
One player at the trial is randomly selected.
What is the probability that the player is from Lithgow and is selected in the representative team?
Give your answer to two decimal places. (2 marks)
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`0.27`
`Ptext{(player is from Lithgow and selected)}`
`= P(A and B)`
`= P(A) xx P(B)\ \ \ \text{(independent events)}`
`= 20/30 xx 8/20`
`= 8/30`
`= 0.27\ \text{(2 d.p.)}`
A coin is tossed 3 times. There are 8 possible outcomes.
What is the probability of getting 2 heads and 1 tail in any order? (2 marks)
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`3/8`
`text(Strategy 1)`
`text{The table (array) below lists the possible outcomes:}`
1st toss | H | H | H | H | T | T | T | T | |
2nd toss | H | H | T | T | H | H | T | T | |
3rd toss | H | T | H | T | H | T | H | T | |
✓ | ✓ | ✓ |
`text(From table,)\ Ptext{(2H, 1T)} = 3/8`
`text(Strategy 2)`
`text(Using a probability tree:)`
A bowl of fruit contains 17 apples of which 9 are red and 8 are green.
Dennis takes one apple at random and eats it. Margaret also takes an apple at random and eats it.
By drawing a probability tree diagram, or otherwise, find the probability that Dennis and Margaret eat apples of the same colour. (3 marks)
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`8/17`
A group of 485 people was surveyed. The people were asked whether or not they smoke. The results are recorded in the table.
A person is selected at random from the group.
What is the approximate probability that the person selected is a smoker OR is male?
`=> C`
`P(text(Smoker or a male))`
`= (text(Total males + female smokers))/(text(Total surveyed))`
`= (264 + 68)/485`
`= 0.684…`
`=> C`
The probability of winning a game is `7/10`.
Which expression represents the probability of winning two consecutive games?
`D`
`text{Since the two events are independent:}`
`P text{(W)}` | `= 7/10` |
`P text{(WW)}` | `= 7/10 xx 7/10` |
`=>D`
A new test has been developed for determining whether or not people are carriers of the Gaussian virus.
Two hundred people are tested. A two-way table is being used to record the results.
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What is the probability that the test results would show this? (2 marks)
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i. `A` | `= 200-(74 + 12 + 16)` |
`= 98` |
ii. `P` | `= text(# Positive carriers)/text(Total carriers)` |
`= 74/86` | |
`= 37/43` |
iii. `text(# People with inaccurate results)`
`= 12 + 16`
`= 28`
On a television game show, viewers voted for their favourite contestant. The results were recorded in the two-way table.
\begin{array} {|l|c|c|}
\hline
\rule{0pt}{2.5ex} \rule[-1ex]{0pt}{0pt} & \textbf{Male viewers} & \textbf{Female viewers} \\
\hline
\rule{0pt}{2.5ex}\textbf{Contestant 1}\rule[-1ex]{0pt}{0pt} & 1372 & 3915\\
\hline
\rule{0pt}{2.5ex}\textbf{Contestant 2}\rule[-1ex]{0pt}{0pt} & 2054 & 3269\\
\hline
\end{array}
One male viewer was selected at random from all of the male viewers.
What is the probability that he voted for Contestant 1?
`C`
`text(Total male viewers)\ = 1372 + 2054= 3426`
`P\ text{(Male viewer chosen voted for C1)}`
`= text(Males who voted for C1)/text(Total male viewers)`
`= 1372/3426`
`=> C`
Lie detector tests are not always accurate. A lie detector test was administered to 200 people.
The results were:
• 50 people lied. Of these, the test indicated that 40 had lied;
• 150 people did NOT lie. Of these, the test indicated that 20 had lied.
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There are 100 tickets sold in a raffle. Justine sold all 100 tickets to five of her friends. The number of tickets she sold to each friend is shown in the table.
Give a reason why Justine’s statement is NOT correct. (1 mark)
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i. `text(The claim is incorrect because each of her friends bought)`
`text(a different number of tickets and therefore their chances of)`
`text(winning are different.)`
ii. `text(Number of tickets not sold to K or H)`
`= 45 + 10 + 14`
`= 69`
`:.\ text(Probability 1st prize NOT won by K or H)`
`= 69/100`
In a stack of 10 DVDs, there are 5 rated PG, 3 rated G and 2 rated M.
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Grant chooses two DVDs at random from the stack. Copy or trace the tree diagram into your writing booklet.
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Leanne copied a two-way table into her book.
Leanne made an error in copying one of the values in the shaded section of the table.
Which value has been incorrectly copied?
`D`
`text(By checking row and column total, the number)`
`text(of females part-time work is incorrect)`
`=> D`
Cecil invited 175 movie critics to preview his new movie. After seeing the movie, he conducted a survey. Cecil has almost completed the two-way table.
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What is the probability that the critic was less than 40 years old and did not like the movie? (2 marks)
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Will this movie be considered a box office success? Justify your answer. (1 mark)
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i. `text{Critics liked and}\ >= 40`
`= 102-65`
`= 37`
`:. A = 37+31=68`
ii. `text{Critics did not like and < 40}`
`= 175-65-37-31`
`= 42`
`:.\ P text{(not like and < 40)}`
`= 42/175`
`= 6/25`
iii. `text(Critics liked) = 102`
`text(% Critics liked)` | `= 102/175 xx 100` |
`= 58.28…%` |
`:.\ text{Movie NOT a box office success (< 65% critics liked)}`
In Mathsville, there are on average eight rainy days in October.
Which expression could be used to find a value for the probability that it will rain on two consecutive days in October in Mathsville?
`D`
`P text{(rains)} = 8/31\ \ \text{(independent event for each day)}`
`text{Since each day has same probability:}`
`P(R_1 R_2) = 8/31 xx 8/31`
`=> D`
A group of 150 people was surveyed and the results recorded.
A person is selected at random from the surveyed group.
What is the probability that the person selected is a male who does not own a mobile?
`A`
`P` | `= text(number of males without mobile)/text(number in group)` |
`= 28/150` |
`=> A`
An unbiased coin is tossed 10 times.
A tail is obtained on each of the first 9 tosses.
What is the probability that a tail is obtained on the 10th toss?
`B`
`text(Each toss is an independent event and has an even chance)`
`text(of being a head or tail.)`
`=> B`
In each of three raffles, 100 tickets are sold and one prize is awarded.
Mary buys two tickets in one raffle. Jane buys one ticket in each of the other two raffles.
Determine who has the better chance of winning at least one prize. Justify your response using probability calculations. (4 marks)
`P(text(Mary wins) )` | `= 2/100` |
`= 1/50` |
`P(text(Jane wins at least 1) )` | `= 1-P (text(loses both) )` |
`= 1-99/100 xx 99/100` | |
`= 1-9801/(10\ 000)` | |
`= 199/(10\ 000)` |
`text{Since}\ \ 1/50 > 199/(10\ 000)`
`=>\ text(Mary has a better chance of winning.)`
`P(text(Mary wins) )` | `= 2/100` |
`= 1/50` |
`P(text(Jane wins at least 1) )` | `= 1-P (text(loses both) )` |
`= 1-99/100 xx 99/100` | |
`= 1-9801/(10\ 000)` | |
`= 199/(10\ 000)` |
`text{Since}\ \ 1/50 > 199/(10\ 000)`
`=>\ text(Mary has a better chance of winning.)`
The probability that Michael will score more than 100 points in a game of bowling is `31/40`.
Is the commentator correct? Give a reason for your answer. (1 mark)
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i. `text(The commentator is incorrect. The correct)`
`text(statement is)\ Ptext{(score} <=100 text{)} =9/40`
`text{(i.e. less than “or equal to 100” is the correct statement)}`
ii. | `\ \ \ P(text{score >100 in both})` | `= 31/40 xx 31/40` |
`= 961/1600` |
Lou and Ali are on a fitness program for one month. The probability that Lou will finish the program successfully is 0.7 while the probability that Ali will finish successfully is 0.6. The probability tree shows this information
What is the probability that only one of them will be successful ?
`D`
`text(Let)\ \ Ptext{(Lou successful)}=P(L) = 0.7, \ P(\text{not}\ L) = 0.3`
`text(Let)\ \ Ptext{(Ali successful)}=P(A) = 0.6, \ P(\text{not}\ A) = 0.4`
`P text{(only 1 successful)}` | `=P(L)xxP(text(not)\ A)+P(text(not)\ L)xxP(A)` |
`=(0.7xx0.4)+(0.3xx0.6)` | |
`=0.28+0.18` | |
`=0.46` |
`=> D`
A box contains 33 scarves made from two different fabrics. There are 14 scarves made from silk (S) and 19 made from wool (W).
Two girls each select, at random, a scarf to wear from the box.
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ii. `P\ text{(2 silk)}` | `= P(S_1) xx P(S_2)` |
`= 14/33 xx 13/32` | |
`= 91/528` |
iii. `P\ text{(different)}` | `= P (S_1,W_2) + P(W_1,S_2)` |
`= (14/33 xx 19/32) + (19/33 xx 14/32)` | |
`= 532/1056` | |
`= 133/264` |
Two unbiased dice, each with faces numbered 1, 2, 3, 4, 5, 6, are rolled.
What is the probability of obtaining a sum of 6?
`D`
`text(Total outcomes)=6xx6=36`
`text{Outcomes that sum to 6}=text{(1,5) (5,1) (2,4) (4,2) (3,3)} =5`
`:.\ P\text{(sum of 6)} =5/36`
`=>\ D`