| Exam Board | AQA |
|---|---|
| Module | AS Paper 2 (AS Paper 2) |
| Year | 2018 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Binomial Distribution |
| Type | Independent binomial samples with compound probability |
| Difficulty | Moderate -0.8 This is a straightforward binomial probability question requiring only standard calculator work (P(Xโฅ3) = 1-P(Xโค2)) and recall of binomial assumptions. Part (b) is simple multiplication of independent probabilities. No problem-solving or novel insight neededโpurely routine application of AS-level probability concepts. |
| Spec | 2.04b Binomial distribution: as model B(n,p)2.04c Calculate binomial probabilities |
| Answer | Marks | Guidance |
|---|---|---|
| 15(a) | Calculates ๐(๐ โค 2) or | |
| ๐(๐ โค 3) using the binomial dist | AO3.4 | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| AWRT 0.448 | AO1.1b | A1 |
| Answer | Marks |
|---|---|
| 15(b) | Calculates the cube of their answer |
| Answer | Marks | Guidance |
|---|---|---|
| their cube. | AO1.1a | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| AWFW 0.0899 to 0.0901) | AO1.1b | A1F |
| Answer | Marks | Guidance |
|---|---|---|
| 15(c) | States first appropriate assumption | |
| in context | AO3.5b | E1 |
| Answer | Marks | Guidance |
|---|---|---|
| trialsโ | AO3.5b | E1 |
| Total | 6 | |
| Q | Marking Instructions | AO |
Question 15:
--- 15(a) ---
15(a) | Calculates ๐(๐ โค 2) or
๐(๐ โค 3) using the binomial dist | AO3.4 | M1 | ๐(๐ โค 2)= 0.55(177โฆ)
(๐(๐ โค 3) = 0.80(589โฆ)
๐(๐ โฅ 3)= 1โ๐(๐ โค 2)= 0.448
Obtains correct answer
AWRT 0.448 | AO1.1b | A1
--- 15(b) ---
15(b) | Calculates the cube of their answer
to (a). Do not accept as part of a
larger calculation or multiples of
their cube. | AO1.1a | M1 | 0.448โฆ3
= 0.090 (3dp)
Obtains correct answer( FT if
AWFW 0.0899 to 0.0901) | AO1.1b | A1F
--- 15(c) ---
15(c) | States first appropriate assumption
in context | AO3.5b | E1 | The probability of hitting the
bullseye is fixed at 0.3
or
Hitting the bullseye with each dart
is independent of hitting the
bullseye with any other dart
or
There are 2 possible outcomes, hit
bullseye or does not hit bullseye
States second appropriate
assumption in context
Accept probability of hitting
bullseye โis constantโ
Do not accept โfixed number of
trialsโ | AO3.5b | E1
Total | 6
Q | Marking Instructions | AO | Marks | Typical SolutionNicola, a darts player, is practising hitting the bullseye. She knows from previous experience that she has a probability of 0.3 of hitting the bullseye with each dart.
Nicola throws eight practice darts.
\begin{enumerate}[label=(\alph*)]
\item Using a binomial distribution, calculate the probability that she will hit the bullseye three or more times. [2 marks]
\item Nicola throws eight practice darts on three different occasions. Calculate the probability that she will hit the bullseye three or more times on all three occasions. [2 marks]
\item State two assumptions that are necessary for the distribution you have used in part (a) to be valid. [2 marks]
\end{enumerate}
\hfill \mbox{\textit{AQA AS Paper 2 2018 Q15 [6]}}