| Exam Board | OCR |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2012 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Binomial Distribution |
| Type | Sum or combination of independent binomial values |
| Difficulty | Standard +0.3 This is a straightforward binomial probability question requiring (i) direct calculation of P(X<2) = P(X=0) + P(X=1) using the binomial formula, and (ii) recognizing that 'exactly one equals 2' means P(X=2)×P(X≠2) + P(X≠2)×P(X=2) = 2P(X=2)P(X≠2). Both parts are standard textbook exercises with clear methods and minimal steps, making it slightly easier than average. |
| Spec | 5.02c Linear coding: effects on mean and variance |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \((1-0.12)^{13}\) or \(13 \times (1-0.12)^{12} \times 0.12\) | M1 | Either seen |
| \((1-0.12)^{13} + 13 \times (1-0.12)^{12} \times 0.12\) | M1 | Fully correct method |
| \(= 0.526\) (3 sf) | A1[3] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(^{13}C_2 \times 0.12^2 \times (1-0.12)^{11}\) | M1 | or \(0.275(\ldots)\) |
| \(2 \times \text{"0.275275"} \times (1 - \text{"0.275275"})\) | M1 | Correct method except allow omit "\(2\times\)" |
| \(= 0.399\) (3 sf) | A1 [3] |
## Question 3:
### Part (i)
| Answer | Marks | Guidance |
|--------|-------|----------|
| $(1-0.12)^{13}$ or $13 \times (1-0.12)^{12} \times 0.12$ | M1 | Either seen | $1 -$ correct terms: M1M0A0 |
| $(1-0.12)^{13} + 13 \times (1-0.12)^{12} \times 0.12$ | M1 | Fully correct method | |
| $= 0.526$ (3 sf) | A1[3] | | |
### Part (ii)
| Answer | Marks | Guidance |
|--------|-------|----------|
| $^{13}C_2 \times 0.12^2 \times (1-0.12)^{11}$ | M1 | or $0.275(\ldots)$ | Allow if $\times$ or $+$ something |
| $2 \times \text{"0.275275"} \times (1 - \text{"0.275275"})$ | M1 | Correct method except allow omit "$2\times$" | NB unlike 2nd M1 in (i) which is for fully correct method |
| $= 0.399$ (3 sf) | A1 [3] | | NB $2 \times 0.12 \times 0.88$: M0M0A0 |
---3 A random variable $X$ has the distribution $\mathrm { B } ( 13,0.12 )$.\\
(i) Find $\mathrm { P } ( X < 2 )$.
Two independent values of $X$ are found.\\
(ii) Find the probability that exactly one of these values is equal to 2 .
\hfill \mbox{\textit{OCR S1 2012 Q3 [6]}}