In the Venn diagram below, shade in the area that represents
`C \cup (B \cap A^{′})` (2 marks)
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Probability, SMB-017
Probability, SMB-016
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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Probability, SMB-015
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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Probability, SMB-014
Students studying vocational education courses were surveyed about their living arrangements.
- One of these students is selected at random. What is the probability, correct to the nearest percentage, that this student is male and living with his parent(s)? (2 marks)
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- A female student is selected. What is the probability that she is not living with her parent(s)? (2 marks)
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Probability, SMB-013
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)
\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} & & 8 \\
\hline
\rule{0pt}{2.5ex}\text{No Motorbike}\rule[-1ex]{0pt}{0pt} & & \\
\hline
\end{array}
\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} & & 8 \\
\hline
\rule{0pt}{2.5ex}\text{No Motorbike}\rule[-1ex]{0pt}{0pt} & & \\
\hline
\end{array}
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Probability, SMB-012
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)
\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} & & \\
\hline
\rule{0pt}{2.5ex}\text{No French}\rule[-1ex]{0pt}{0pt} & 8 & \\
\hline
\end{array}
\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} & & \\
\hline
\rule{0pt}{2.5ex}\text{No French}\rule[-1ex]{0pt}{0pt} & 8 & \\
\hline
\end{array}
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Probability, SMB-011
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)
\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} & & \\
\hline
\rule{0pt}{2.5ex}\text{No Cat}\rule[-1ex]{0pt}{0pt} & & 8\\
\hline
\end{array}
\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} & & \\
\hline
\rule{0pt}{2.5ex}\text{No Cat}\rule[-1ex]{0pt}{0pt} & & 8\\
\hline
\end{array}
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Probability, SMB-010
In the Venn diagram below, shade in the area that represents
`A \cap B \cap C` (2 marks)
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Probability, SMB-009
In the Venn diagram below, shade in the area that represents
`B^c \cap C^c` (2 marks)
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Probability, SMB-008
In the Venn diagram below, shade in the area that represents
`(A \cap B) \cup C` (2 marks)
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Probability, SMB-007
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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Probability, SMB-006
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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Probability, SMB-005 MC
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?
- `2`
- `24`
- `26`
- `54`
Probability, SMB-004
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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Probability, SMB-003 MC
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?
- `40/120`
- `60/120`
- `80/120`
- `100/120`
Probability, SMB-002 MC
The table below shows all the people at Angus' birthday party.
What fraction of the children at the party are female?
- `20/60`
- `45/60`
- `20/100`
- `45/100`
Probability, SMB-001
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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Probability, STD2 S2 2016 HSC 23 MC
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?
- 33%
- 18%
- 68%
- 87%
Probability, STD2 S2 2006 HSC 26c
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.
- What is the value of `A`? (1 mark)
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- A person selected from the tested group is a carrier of the virus.
What is the probability that the test results would show this? (2 marks)
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- For how many of the people tested were their test results inaccurate? (1 mark)
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Probability, STD2 S2 2005 HSC 16 MC
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?
- `1372/(10\ 610)`
- `1372/5287`
- `1372/3426`
- `1372/2054`
Probability, STD2 S2 2004 HSC 25c
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.
- Complete the table using the information above (2 marks)
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- For how many of the people tested was the lie detector test accurate? (1 mark)
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- For what percentage of the people tested was the test accurate? (1 mark)
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- What is the probability that the test indicated a lie for a person who did NOT lie? (1 mark)
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i.
ii. `text(# Accurate readings)`
`= 40 + 130`
`= 170`
iii. `text(Percentage of people with accurate readings)`
`= text(# Accurate readings)/text(Total readings) xx 100`
`= 170/200`
`= 85 text(%)`
iv. `text{P(lie detected when NOT a lie)}`
`= 20/150`
`= 2/15`
Probability, STD2 S2 2007 HSC 16 MC
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?
- The number of males in full-time work
- The number of males in part-time work
- The number of females in full-time work
- The number of females in part-time work
Probability, STD2 S2 2008 HSC 26a
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.
- Determine the value of `A`. (1 mark)
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- A movie critic is selected at random.
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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- Cecil believes that his movie will be a box office success if 65% of the critics who were surveyed liked the movie.
Will this movie be considered a box office success? Justify your answer. (1 mark)
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Probability, STD2 S2 2014 HSC 8 MC
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?
- `28/150`
- `45/150`
- `28/70`
- `45/70`