Question 6 - A-Level Maths

OCR MEI S1 — Question 6 4 marks

Exam Board	OCR MEI
Module	S1 (Statistics 1)
Marks	4
Paper	Download PDF ↗
Mark scheme	Download PDF ↗
Topic	Independent Events
Type	Test independence using definition
Difficulty	Moderate -0.8 This is a straightforward probability question requiring counting outcomes from a given table and checking independence using P(A∩B) = P(A)P(B). Part (i) is simple counting, and part (ii) involves routine application of the independence formula with no conceptual challenges—easier than average A-level content.
Spec	2.03a Mutually exclusive and independent events

The table shows all the possible products of the scores on two fair four-sided dice. \includegraphics{figure_6}

Find the probability that the product of the two scores is less than 10. [1]
Show that the events 'the score on the first die is even' and 'the product of the scores on the two dice is less than 10' are not independent. [3]

Show mark scheme Show mark scheme source

Question 6:

(i) ---

6

Answer	Marks
(i)	13

P(product of two scores < 10) = = 0.8125

Answer	Marks	Guidance
16	B1	1
(ii)	13 13

P(even)  P(< 10) = 0.5  = = 0.40625

16 32

6 P(even ∩ < 10) = = 0.375

16

Answer	Marks
So not independent.	13 13

M1 for 0.5  or

16 32

FT their answer to (i)

6 M1 for

16

Answer	Marks	Guidance
A1	3	Do not allow these embedded in probability formulae
Also allow P(even	<10) = 6/13≠ P(even) = 1/2
Or P(<10	even) = 6/8≠ P(<10) = 13/16
Or P(even	<10) = 6/13≠ P(even	<10’) = 2/3
Or P(<10	even) = 6/8≠ P(<10	even’) = 7/8

For all of these alternatives allow M2 for both

probabilities. (M1 not available except if they correctly

Answer	Marks
state both probabilities EG P(even	<10) and P(even)

and get one correct)

If they do not state what probabilities they are finding,

give M2 for one of the above pairs of probabilities

with ≠ symbol

Answer	Marks
TOTAL	4

Question 6:
--- 6
(i) ---
6
(i) | 13
P(product of two scores < 10) = = 0.8125
16 | B1 | 1 | Allow 0.813 or 0.812
(ii) | 13 13
P(even)  P(< 10) = 0.5  = = 0.40625
16 32
6
P(even ∩ < 10) = = 0.375
16
So not independent. | 13 13
M1 for 0.5  or
16 32
FT their answer to (i)
6
M1 for
16
A1 | 3 | Do not allow these embedded in probability formulae
Also allow P(even|<10) = 6/13≠ P(even) = 1/2
Or P(<10|even) = 6/8≠ P(<10) = 13/16
Or P(even|<10) = 6/13≠ P(even|<10’) = 2/3
Or P(<10|even) = 6/8≠ P(<10|even’) = 7/8
For all of these alternatives allow M2 for both
probabilities. (M1 not available except if they correctly
state both probabilities EG P(even|<10) and P(even)
and get one correct)
If they do not state what probabilities they are finding,
give M2 for one of the above pairs of probabilities
with ≠ symbol
TOTAL | 4

Show LaTeX source

The table shows all the possible products of the scores on two fair four-sided dice.

\includegraphics{figure_6}

\begin{enumerate}[label=(\roman*)]
\item Find the probability that the product of the two scores is less than 10. [1]
\item Show that the events 'the score on the first die is even' and 'the product of the scores on the two dice is less than 10' are not independent. [3]
\end{enumerate}

\hfill \mbox{\textit{OCR MEI S1  Q6 [4]}}

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