| Exam Board | Edexcel |
|---|---|
| Module | S2 (Statistics 2) |
| Session | Specimen |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Binomial Distribution |
| Type | Basic E(X) and Var(X) calculation |
| Difficulty | Moderate -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. |
| Spec | 2.04b 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
\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]}}