SPS SPS FM Statistics 2021 September — Question 3 11 marks

Exam BoardSPS
ModuleSPS FM Statistics (SPS FM Statistics)
Year2021
SessionSeptember
Marks11
TopicTree Diagrams
TypeConditional probability tree diagram
DifficultyModerate -0.8 This is a straightforward conditional probability question requiring a tree diagram and basic probability calculations. The independence test in part (c) is standard A-level content. All steps are routine applications of probability rules with no novel problem-solving required, making it easier than average.
Spec2.03a Mutually exclusive and independent events2.03b Probability diagrams: tree, Venn, sample space2.03c Conditional probability: using diagrams/tables
A group of students were surveyed by a principal and \(\frac{2}{3}\) were found to always hand in assignments on time. When questioned about their assignments \(\frac{3}{5}\) said they always start their assignments on the day they are issued and, of those who always start their assignments on the day they are issued, \(\frac{11}{20}\) hand them in on time.
  1. Draw a tree diagram to represent this information. [3 marks]
  2. Find the probability that a randomly selected student:
    1. always start their assignments on the day they are issued and hand them in on time. [2 marks]
    2. does not always hand in assignments on time and does not start their assignments on the day they are issued. [4 marks]
  3. Determine whether or not always starting assignments on the day they are issued and handing them in on time are statistically independent. Give reasons for your answer. [2 marks]
A group of students were surveyed by a principal and $\frac{2}{3}$ were found to always hand in assignments on time. When questioned about their assignments $\frac{3}{5}$ said they always start their assignments on the day they are issued and, of those who always start their assignments on the day they are issued, $\frac{11}{20}$ hand them in on time.

\begin{enumerate}[label=(\alph*)]
\item Draw a tree diagram to represent this information.
[3 marks]

\item Find the probability that a randomly selected student:
\begin{enumerate}[label=(\roman*)]
\item always start their assignments on the day they are issued and hand them in on time.
[2 marks]

\item does not always hand in assignments on time and does not start their assignments on the day they are issued.
[4 marks]
\end{enumerate}

\item Determine whether or not always starting assignments on the day they are issued and handing them in on time are statistically independent. Give reasons for your answer.
[2 marks]
\end{enumerate}

\hfill \mbox{\textit{SPS SPS FM Statistics 2021 Q3 [11]}}
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