| Exam Board | OCR MEI |
|---|---|
| Module | Further Statistics A AS (Further Statistics A AS) |
| Year | 2020 |
| Session | November |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Geometric Distribution |
| Type | Second success on trial n |
| Difficulty | Moderate -0.3 This is a straightforward application of geometric and binomial distribution formulas with clear parameters (p=12/52=3/13). Parts (a) and (c) are direct formula substitutions for geometric distribution, (b) uses complement rule, and (d) requires binomial calculation. All parts are standard textbook exercises requiring recall and basic computation rather than problem-solving insight. |
| Spec | 2.04a Discrete probability distributions2.04b Binomial distribution: as model B(n,p)2.04c Calculate binomial probabilities5.02f Geometric distribution: conditions5.02g Geometric probabilities: P(X=r) = p(1-p)^(r-1)5.02h Geometric: mean 1/p and variance (1-p)/p^2 |
| Answer | Marks | Guidance |
|---|---|---|
| 3 | (a) | P(Sixth try) = |
| Answer | Marks |
|---|---|
| �13� �13� | M1 |
| Answer | Marks |
|---|---|
| [2] | 3.3 |
| Answer | Marks | Guidance |
|---|---|---|
| 3 | (b) | P(at least once in first six) = |
| Answer | Marks |
|---|---|
| 1−�13� | M1 |
| Answer | Marks |
|---|---|
| [2] | 1.1a |
| Answer | Marks | Guidance |
|---|---|---|
| 3 | (c) | P(second time sixth try) = |
| Answer | Marks |
|---|---|
| 5�13� �13� | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| [2] | 3.1b | |
| 1.1 | Allow M1 if 5 omitted | |
| 3 | (d) | P(at least 2) = 1 – 0.5801 |
| = 0.4199 | M1 |
| Answer | Marks |
|---|---|
| [2] | 3.1b |
| 1.1 | M1 for 1 – P(X = 0 or 1) using |
Question 3:
3 | (a) | P(Sixth try) =
5
10 3
= 0.0622
�13� �13� | M1
A1
[2] | 3.3
1.1
3 | (b) | P(at least once in first six) =
6
= 0.792180
1−�13� | M1
A1
[2] | 1.1a
1.1
3 | (c) | P(second time sixth try) =
4 2
= 0.093120 3
5�13� �13� | M1
A1
[2] | 3.1b
1.1 | Allow M1 if 5 omitted
3 | (d) | P(at least 2) = 1 – 0.5801
= 0.4199 | M1
A1
[2] | 3.1b
1.1 | M1 for 1 – P(X = 0 or 1) using
B(6, 3/13)
BC3 A child is trying to draw court cards from an ordinary pack of 52 cards (court cards are Kings, Queens and Jacks; there are 12 in a pack). She draws cards, one at a time, with replacement, from the pack.
Find the probabilities of the following events.
\begin{enumerate}[label=(\alph*)]
\item She draws a court card for the first time on the sixth try.
\item She draws a court card at least once in the first six tries.
\item She draws a court card for the second time on the sixth try.
\item She draws at least two court cards in the first six tries.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Further Statistics A AS 2020 Q3 [8]}}