Edexcel S1 2002 November — Question 2 7 marks

Exam BoardEdexcel
ModuleS1 (Statistics 1)
Year2002
SessionNovember
Marks7
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TopicProbability Definitions
TypeMulti-item selection from population
DifficultyModerate -0.8 This is a straightforward probability question testing basic combinations and the concept of sampling without replacement. Part (a) requires a simple calculation of P(3 arts students) = (60/125)(59/124)(58/123), and part (b) requires organizing cases for 'exactly one science student' using similar multiplication. The setup is clear, the arithmetic is routine, and no conceptual insight beyond standard S1 techniques is needed, making this easier than average.
Spec2.03a Mutually exclusive and independent events5.01a Permutations and combinations: evaluate probabilities

There are 125 sixth-form students in a college, of whom 60 are studying only arts subjects, 40 only science subjects and the rest a mixture of both. Three students are selected at random, without replacement. Find the probability that
  1. all three students are studying only arts subjects, [4]
  2. exactly one of the three students is studying only science subjects. [3]

There are 125 sixth-form students in a college, of whom 60 are studying only arts subjects, 40 only science subjects and the rest a mixture of both.

Three students are selected at random, \textit{without replacement}.

Find the probability that

\begin{enumerate}[label=(\alph*)]
\item all three students are studying only arts subjects, [4]

\item exactly one of the three students is studying only science subjects. [3]
\end{enumerate}

\hfill \mbox{\textit{Edexcel S1 2002 Q2 [7]}}