Edexcel S2 — Question 4 12 marks

Exam BoardEdexcel
ModuleS2 (Statistics 2)
Marks12
PaperDownload PDF ↗
TopicGeometric Distribution
TypeGeometric then binomial separate scenarios
DifficultyModerate -0.3 This is a straightforward S2 question testing basic knowledge of binomial conditions (bookwork) and standard geometric/binomial probability calculations. The die bias setup requires simple probability calculation (p=2/7), then applying standard formulas. Part (a) is pure recall, parts (b) and (c) are routine applications with no novel problem-solving required, making this slightly easier than average.
Spec2.04b Binomial distribution: as model B(n,p)5.02f Geometric distribution: conditions5.02g Geometric probabilities: P(X=r) = p(1-p)^(r-1)

  1. Write down the conditions under which the binomial distribution may be a suitable model to use in statistical work. [4]
A six-sided die is biased. When the die is thrown the number 5 is twice as likely to appear as any other number. All the other faces are equally likely to appear. The die is thrown repeatedly. Find the probability that
  1. the first 5 will occur on the sixth throw, [8]
  2. in the first eight throws there will be exactly three 5s.

\begin{enumerate}[label=(\alph*)]
\item Write down the conditions under which the binomial distribution may be a suitable model to use in statistical work. [4]
\end{enumerate}

A six-sided die is biased. When the die is thrown the number 5 is twice as likely to appear as any other number. All the other faces are equally likely to appear. The die is thrown repeatedly.

Find the probability that

\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item the first 5 will occur on the sixth throw, [8]
\item in the first eight throws there will be exactly three 5s.
\end{enumerate}

\hfill \mbox{\textit{Edexcel S2  Q4 [12]}}