OCR S1 2008 January — Question 7 8 marks

Exam BoardOCR
ModuleS1 (Statistics 1)
Year2008
SessionJanuary
Marks8
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicBinomial Distribution
TypeFinding binomial parameters from properties
DifficultyStandard +0.3 Part (i) tests basic understanding of binomial conditions and definitions (routine recall). Part (ii) requires equating two binomial probabilities and solving for p, which involves algebraic manipulation of the binomial formula but is a standard textbook exercise with a clear method. The algebra is straightforward once the common factors cancel.
Spec2.04b Binomial distribution: as model B(n,p)2.04c Calculate binomial probabilities

7
  1. Andrew plays 10 tennis matches. In each match he either wins or loses.
    1. State, in this context, two conditions needed for a binomial distribution to arise.
    2. Assuming these conditions are satisfied, define a variable in this context which has a binomial distribution.
    3. The random variable \(X\) has the distribution \(\mathrm { B } ( 21 , p )\), where \(0 < p < 1\). Given that \(\mathrm { P } ( X = 10 ) = \mathrm { P } ( X = 9 )\), find the value of \(p\).

7 (i) Andrew plays 10 tennis matches. In each match he either wins or loses.
\begin{enumerate}[label=(\alph*)]
\item State, in this context, two conditions needed for a binomial distribution to arise.
\item Assuming these conditions are satisfied, define a variable in this context which has a binomial distribution.\\
(ii) The random variable $X$ has the distribution $\mathrm { B } ( 21 , p )$, where $0 < p < 1$.

Given that $\mathrm { P } ( X = 10 ) = \mathrm { P } ( X = 9 )$, find the value of $p$.
\end{enumerate}

\hfill \mbox{\textit{OCR S1 2008 Q7 [8]}}