Edexcel S1 2009 June — Question 2 11 marks

Exam BoardEdexcel
ModuleS1 (Statistics 1)
Year2009
SessionJune
Marks11
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicTree Diagrams
TypePopulation partition tree diagram
DifficultyEasy -1.2 This is a straightforward tree diagram question requiring basic probability rules (multiplication along branches, addition across outcomes) and conditional probability using Bayes' theorem. All methods are standard S1 techniques with no conceptual challenges—purely mechanical application of formulas with simple fractions.
Spec2.03b Probability diagrams: tree, Venn, sample space2.03c Conditional probability: using diagrams/tables2.03d Calculate conditional probability: from first principles

2. On a randomly chosen day the probability that Bill travels to school by car, by bicycle or on foot is \(\frac { 1 } { 2 } , \frac { 1 } { 6 }\) and \(\frac { 1 } { 3 }\) respectively. The probability of being late when using these methods of travel is \(\frac { 1 } { 5 } , \frac { 2 } { 5 }\) and \(\frac { 1 } { 10 }\) respectively.
  1. Draw a tree diagram to represent this information.
  2. Find the probability that on a randomly chosen day
    1. Bill travels by foot and is late,
    2. Bill is not late.
  3. Given that Bill is late, find the probability that he did not travel on foot.

2. On a randomly chosen day the probability that Bill travels to school by car, by bicycle or on foot is $\frac { 1 } { 2 } , \frac { 1 } { 6 }$ and $\frac { 1 } { 3 }$ respectively. The probability of being late when using these methods of travel is $\frac { 1 } { 5 } , \frac { 2 } { 5 }$ and $\frac { 1 } { 10 }$ respectively.
\begin{enumerate}[label=(\alph*)]
\item Draw a tree diagram to represent this information.
\item Find the probability that on a randomly chosen day
\begin{enumerate}[label=(\roman*)]
\item Bill travels by foot and is late,
\item Bill is not late.
\end{enumerate}\item Given that Bill is late, find the probability that he did not travel on foot.
\end{enumerate}

\hfill \mbox{\textit{Edexcel S1 2009 Q2 [11]}}