| Exam Board | OCR MEI |
|---|---|
| Module | Paper 2 (Paper 2) |
| Year | 2018 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Binomial Distribution |
| Type | Direct binomial probability calculation |
| Difficulty | Moderate -0.8 This is a straightforward application of the binomial distribution formula requiring only direct calculation of P(X=14) and P(X≥14) with clearly stated parameters (n=20, p=0.7). It involves standard calculator work with no conceptual challenges, making it easier than average but not trivial since it requires correct setup and summation for part (ii). |
| Spec | 2.04b Binomial distribution: as model B(n,p)2.04c Calculate binomial probabilities |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Use of \(B\sim(20, 0.7)\) soi | M1 (AO3.1b) | |
| \(0.191638982753\ldots\) rounded to 2 or more dp isw BC | A1 (AO1.1) | NB 0.1916 or 0.192 or 0.19 |
| [2] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(P(X\leq 13)\) found soi | M1 (AO3.1b) | NB 0.391990188187; M0 if \(P(X=13)\) used NB 0.1643…; if M0 allow SC1 for \(1-P(X\leq14)=1-0.58362\ldots=0.41637083\) rounded to 2 or more dp |
| \(0.608009811813\ldots\) rounded to 2 or more dp isw BC | A1 (AO1.1) | NB 0.6080 or 0.608 or 0.61 |
| [2] |
## Question 8(i):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Use of $B\sim(20, 0.7)$ soi | M1 (AO3.1b) | |
| $0.191638982753\ldots$ rounded to 2 or more dp isw BC | A1 (AO1.1) | NB 0.1916 or 0.192 or 0.19 |
| **[2]** | | |
## Question 8(ii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $P(X\leq 13)$ found soi | M1 (AO3.1b) | NB 0.391990188187; M0 if $P(X=13)$ used NB 0.1643…; if M0 allow SC1 for $1-P(X\leq14)=1-0.58362\ldots=0.41637083$ rounded to 2 or more dp |
| $0.608009811813\ldots$ rounded to 2 or more dp isw BC | A1 (AO1.1) | NB 0.6080 or 0.608 or 0.61 |
| **[2]** | | |
---8 Every morning before breakfast Laura and Mike play a game of chess. The probability that Laura wins is 0.7 . The outcome of any particular game is independent of the outcome of other games. Calculate the probability that, in the next 20 games,\\
(i) Laura wins exactly 14 games,\\
(ii) Laura wins at least 14 games.
\hfill \mbox{\textit{OCR MEI Paper 2 2018 Q8 [4]}}