Edexcel S2 Specimen — Question 3 7 marks

Exam BoardEdexcel
ModuleS2 (Statistics 2)
SessionSpecimen
Marks7
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicBinomial Distribution
TypeBasic E(X) and Var(X) calculation
DifficultyModerate -0.3 This is a straightforward application of binomial distribution with clearly stated parameters (p=0.25, n=20 then n=100). Parts (a) and (b) require direct calculation using binomial probability formulas or tables, while part (c) is simple recall of E(X)=np. The setup is transparent and all parts are routine textbook exercises requiring no problem-solving insight, making it slightly easier than average.
Spec2.04b Binomial distribution: as model B(n,p)2.04c Calculate binomial probabilities

A manufacturer of chocolates produces 3 times as many soft centred chocolates as hard centred ones. Assuming that chocolates are randomly distributed within boxes of chocolates, find the probability that in a box containing 20 chocolates there are
  1. equal numbers of soft centred and hard centred chocolates, [3]
  2. fewer than 5 hard centred chocolates. [2]
A large box of chocolates contains 100 chocolates.
  1. Write down the expected number of hard centred chocolates in a large box. [2]

A manufacturer of chocolates produces 3 times as many soft centred chocolates as hard centred ones.

Assuming that chocolates are randomly distributed within boxes of chocolates, find the probability that in a box containing 20 chocolates there are

\begin{enumerate}[label=(\alph*)]
\item equal numbers of soft centred and hard centred chocolates, [3]
\item fewer than 5 hard centred chocolates. [2]
\end{enumerate}

A large box of chocolates contains 100 chocolates.

\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Write down the expected number of hard centred chocolates in a large box. [2]
\end{enumerate}

\hfill \mbox{\textit{Edexcel S2  Q3 [7]}}