| Exam Board | Edexcel |
|---|---|
| Module | S2 (Statistics 2) |
| Session | Specimen |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Topic | Binomial Distribution |
| Type | E(X) and Var(X) with probability calculations |
| Difficulty | Moderate -0.3 This is a straightforward binomial distribution question requiring standard calculations: direct use of binomial probability formula for parts (a)-(b), recall of E(X)=np and Var(X)=np(1-p) for part (c), and routine normal approximation for part (d). All techniques are textbook exercises with no problem-solving insight required, making it slightly easier than average. |
| Spec | 2.04d Normal approximation to binomial5.02b Expectation and variance: discrete random variables5.02c Linear coding: effects on mean and variance5.02d Binomial: mean np and variance np(1-p) |
2. Bhim and Joe play each other at badminton and for each game, independently of all others, the probability that Bhim loses is 0.2
Find the probability that, in 9 games, Bhim loses
\begin{enumerate}[label=(\alph*)]
\item exactly 3 of the games,
\item fewer than half of the games.
Bhim attends coaching sessions for 2 months. After completing the coaching, the probability that he loses each game, independently of all others, is 0.05
Bhim and Joe agree to play a further 60 games.
\item Calculate the mean and variance for the number of these 60 games that Bhim loses.
\item Using a suitable approximation calculate the probability that Bhim loses more than 4 games.
\end{enumerate}
\hfill \mbox{\textit{Edexcel S2 Q2 [10]}}