| Exam Board | SPS |
|---|---|
| Module | SPS SM (SPS SM) |
| Year | 2021 |
| Session | January |
| Marks | 5 |
| Topic | Binomial Distribution |
| Type | Two-stage binomial problems |
| Difficulty | Standard +0.3 This is a straightforward two-stage problem: part (a) requires basic probability distribution setup using given symmetry conditions (routine algebra), and part (b) is a standard binomial probability calculation with n=60, requiring P(X>30). While the calculation involves large numbers, this is a textbook application of binomial distribution with no conceptual challenges or novel problem-solving required. |
| Spec | 2.04a Discrete probability distributions2.04c Calculate binomial probabilities |
7.
A biased spinner can only land on one of the numbers $1,2,3$ or 4 . The random variable $X$ represents the number that the spinner lands on after a single spin and $\mathrm { P } ( X = r ) = \mathrm { P } ( X = r + 2 )$ for $r = 1,2$
Given that $\mathrm { P } ( X = 2 ) = 0.35$
\begin{enumerate}[label=(\alph*)]
\item find the complete probability distribution of $X$.
Ambroh spins the spinner 60 times.
\item Find the probability that more than half of the spins land on the number 4 Give your answer to 3 significant figures.
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM 2021 Q7 [5]}}