| Exam Board | OCR MEI |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Geometric Distribution |
| Type | P(X ≤ n) or P(X < n) |
| Difficulty | Moderate -0.8 This is a straightforward application of geometric distribution formulas with no conceptual complications. Part (i) requires direct substitution into P(X=n) = (1-p)^(n-1) × p, and part (ii) uses P(X≤10) = 1-(1-p)^10. Both are standard textbook exercises requiring only recall and basic calculation, making this easier than average. |
| Spec | 5.02f Geometric distribution: conditions5.02g Geometric probabilities: P(X=r) = p(1-p)^(r-1) |
| Answer | Marks | Guidance |
|---|---|---|
| \(\left(\frac{5}{6}\right)^2 \times \frac{1}{6} = \frac{25}{216} = 0.116\) | M1, M1, A1 [3] | M1 for \(\frac{5}{6}\) (or \(1 - \frac{1}{6}\)) seen; M1 for whole product; cao; Allow 0.12 with working |
| Answer | Marks | Guidance |
|---|---|---|
| \(1 - \left(\frac{5}{6}\right)^{10} = 1 - 0.1615 = 0.8385\) | M1, A1 [2] | M1 for \(\left(\frac{5}{6}\right)^{10}\) without extra terms; cao; Allow 0.838 or 0.839 without working and 0.84 with working |
## Question 6:
**(i)**
$\left(\frac{5}{6}\right)^2 \times \frac{1}{6} = \frac{25}{216} = 0.116$ | M1, M1, A1 [3] | M1 for $\frac{5}{6}$ (or $1 - \frac{1}{6}$) seen; M1 for whole product; cao; Allow 0.12 with working
**(ii)**
$1 - \left(\frac{5}{6}\right)^{10} = 1 - 0.1615 = 0.8385$ | M1, A1 [2] | M1 for $\left(\frac{5}{6}\right)^{10}$ without extra terms; cao; Allow 0.838 or 0.839 without working and 0.84 with working6 Malik is playing a game in which he has to throw a 6 on a fair six-sided die to start the game. Find the probability that\\
(i) Malik throws a 6 for the first time on his third attempt,\\
(ii) Malik needs at most ten attempts to throw a 6.
\hfill \mbox{\textit{OCR MEI S1 Q6 [5]}}