| Exam Board | Edexcel |
|---|---|
| Module | S2 (Statistics 2) |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Topic | Geometric Distribution |
| Type | Geometric then binomial separate scenarios |
| Difficulty | Moderate -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. |
| Spec | 2.04b Binomial distribution: as model B(n,p)5.02f Geometric distribution: conditions5.02g Geometric probabilities: P(X=r) = p(1-p)^(r-1) |
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\item Write down the conditions under which the binomial distribution may be a suitable model to use in statistical work. [4]
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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
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\item the first 5 will occur on the sixth throw, [8]
\item in the first eight throws there will be exactly three 5s.
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\hfill \mbox{\textit{Edexcel S2 Q4 [12]}}