| Exam Board | SPS |
|---|---|
| Module | SPS SM Statistics (SPS SM Statistics) |
| Year | 2023 |
| Session | January |
| Marks | 6 |
| Topic | Probability Definitions |
| Type | Two-way table probabilities |
| Difficulty | Easy -1.8 This is a straightforward two-way table completion exercise requiring only basic arithmetic (subtraction to find missing values) and simple probability calculations (favorable/total). The random sampling part tests only basic understanding of random number generation. No problem-solving insight or complex reasoning required—purely routine recall and application of definitions. |
| Spec | 2.01c Sampling techniques: simple random, opportunity, etc2.03a Mutually exclusive and independent events2.03c Conditional probability: using diagrams/tables |
| \cline { 2 - 4 } \multicolumn{1}{c|}{} | Town | |||
| \cline { 2 - 4 } \multicolumn{1}{c|}{} | A | B | C | Total |
| adult | ||||
| child | ||||
| Total | ||||
2.
Jane conducted a survey. She chose a sample of people from three towns, A, B and C. She noted the following information.
400 people were chosen.\\
230 people were adults.\\
55 adults were from town A .\\
65 children were from town A .\\
35 children were from town B .\\
150 people were from town $B$.
\begin{enumerate}[label=(\alph*)]
\item In the Printed Answer Booklet, complete the two-way frequency table.
\begin{center}
\begin{tabular}{ | l | c | c | c | c | }
\cline { 2 - 4 }
\multicolumn{1}{c|}{} & \multicolumn{3}{c|}{Town} & \multicolumn{1}{c}{} \\
\cline { 2 - 4 }
\multicolumn{1}{c|}{} & A & B & C & Total \\
\hline
adult & & & & \\
\hline
child & & & & \\
\hline
Total & & & & \\
\hline
\end{tabular}
\end{center}
\item One of the people is chosen at random.
\begin{enumerate}[label=(\roman*)]
\item Find the probability that this person is an adult from town A .
\item Given that the person is from town A , find the probability that the person is an adult.
For another survey, Jane wanted to choose a random sample from the 820 students living in a particular hostel. She numbered the students from 1 to 820 and then generated some random numbers on her calculator.
The random numbers were 0.114287562 and 0.081859817 .\\
Jane's friend Kareem used these figures to write down the following sample of five student numbers.
114, 142, 428, 287 and 756\\
Jane used the same figures to write down the following sample of five student numbers.\\
$114,287,562,81$ and 817
\end{enumerate}\item \begin{enumerate}[label=(\roman*)]
\item State, with a reason, which one of these samples is not random.
\item Explain why Jane omitted the number 859 from her sample.
\end{enumerate}\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM Statistics 2023 Q2 [6]}}