| Exam Board | Edexcel |
|---|---|
| Module | AS Paper 2 (AS Paper 2) |
| Year | 2019 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Binomial Distribution |
| Type | Direct binomial probability calculation |
| Difficulty | Moderate -0.8 This is a straightforward binomial probability question requiring only direct application of the binomial distribution formula or calculator functions. Part (a) is trivial recall, while parts (b)(i) and (b)(ii) involve standard cumulative probability calculations with clearly defined parameters (n=28, p=0.2) that students would typically compute using tables or calculator functions with minimal problem-solving required. |
| Spec | 2.04a Discrete probability distributions2.04b Binomial distribution: as model B(n,p)2.04c Calculate binomial probabilities |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| (Discrete) uniform (distribution) | B1 | Continuous uniform is B0 |
| (1) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(B(28,\ 0.2)\) | B1 | Allow B, bin or binomial. May be implied by one correct answer or sight of one correct probability i.e. awrt 0.678, awrt 0.818 or awrt 0.160. \(B(0.2, 28)\) is B0 unless used correctly |
| (1) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(P(X \geq 7) = 1 - P(X \leq 6) \ [= 1 - 0.6784\ldots]\) | M1 | Writing or using \(1 - P(X \leq 6)\) or \(1 - P(X < 7)\) |
| awrt \(\mathbf{0.322}\) | A1 | Correct answer only scores M1A1 |
| (2) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(P(4 \leq X < 8) = P(X \leq 7) - P(X \leq 3) \ [= 0.818\ldots - 0.160\ldots]\) | M1 | Writing or using \(P(X \leq 7) - P(X \leq 3)\), or \(P(X<8)-P(X<4)\), or \(P(X=4)+P(X=5)+P(X=6)+P(X=7)\). Condone \(P(4)\) as \(P(X=4)\) etc. |
| awrt \(\mathbf{0.658}\) | A1 | Correct answer only scores M1A1 |
| (2) |
## Question 3:
### Part (a)
| Answer/Working | Mark | Guidance |
|---|---|---|
| (Discrete) uniform (distribution) | B1 | Continuous uniform is B0 |
| | **(1)** | |
### Part (b)
| Answer/Working | Mark | Guidance |
|---|---|---|
| $B(28,\ 0.2)$ | B1 | Allow B, bin or binomial. May be implied by one correct answer or sight of one correct probability i.e. awrt 0.678, awrt 0.818 or awrt 0.160. $B(0.2, 28)$ is B0 unless used correctly |
| | **(1)** | |
### Part (b)(i)
| Answer/Working | Mark | Guidance |
|---|---|---|
| $P(X \geq 7) = 1 - P(X \leq 6) \ [= 1 - 0.6784\ldots]$ | M1 | Writing or using $1 - P(X \leq 6)$ or $1 - P(X < 7)$ |
| awrt $\mathbf{0.322}$ | A1 | Correct answer only scores M1A1 |
| | **(2)** | |
### Part (b)(ii)
| Answer/Working | Mark | Guidance |
|---|---|---|
| $P(4 \leq X < 8) = P(X \leq 7) - P(X \leq 3) \ [= 0.818\ldots - 0.160\ldots]$ | M1 | Writing or using $P(X \leq 7) - P(X \leq 3)$, or $P(X<8)-P(X<4)$, or $P(X=4)+P(X=5)+P(X=6)+P(X=7)$. Condone $P(4)$ as $P(X=4)$ etc. |
| awrt $\mathbf{0.658}$ | A1 | Correct answer only scores M1A1 |
| | **(2)** | |\begin{enumerate}
\item A fair 5 -sided spinner has sides numbered $1,2,3,4$ and 5
\end{enumerate}
The spinner is spun once and the score of the side it lands on is recorded.\\
(a) Write down the name of the distribution that can be used to model the score of the side it lands on.
The spinner is spun 28 times.\\
The random variable $X$ represents the number of times the spinner lands on 2\\
(b) (i) Find the probability that the spinner lands on 2 at least 7 times.\\
(ii) Find $\mathrm { P } ( 4 \leqslant X < 8 )$
\hfill \mbox{\textit{Edexcel AS Paper 2 2019 Q3 [6]}}