OCR PURE — Question 12 4 marks

Exam BoardOCR
ModulePURE
Marks4
PaperDownload PDF ↗
TopicTree Diagrams
TypeSequential dependent events
DifficultyModerate -0.5 This is a straightforward two-stage probability problem requiring reading values from a Venn diagram and applying the multiplication rule for dependent events without replacement. The calculation involves simple arithmetic with fractions (selecting from 100 then 99 students), making it slightly easier than average but still requiring careful attention to the 'Geography but not Psychology' condition.
Spec2.03a Mutually exclusive and independent events2.03b Probability diagrams: tree, Venn, sample space
12 The Venn diagram shows the numbers of students studying various subjects, in a year group of 100 students. \includegraphics[max width=\textwidth, alt={}, center]{68f1107f-f188-4698-934e-8fd593b25418-7_554_910_347_244} A student is chosen at random from the 100 students. Then another student is chosen from the remaining students. Find the probability that the first student studies History and the second student studies Geography but not Psychology. \section*{END OF QUESTION PAPER} \section*{OCR} Oxford Cambridge and RSA
Question 12:
AnswerMarks Guidance
Answer/WorkingMark Guidance
\(P(\text{1st HGP}' \& \text{2nd GP}')\) or \((\text{1st HGP} \& \text{2nd GP}')\) or \((\text{1st HG}' \& \text{2nd GP}')\)M1 One of the following expressions seen
\(= \dfrac{25}{100} \times \dfrac{36}{99} + \dfrac{3}{100} \times \dfrac{37}{99} + \dfrac{15}{100} \times \dfrac{37}{99}\)M1 Another expression seen: \(\dfrac{25}{100} \times \dfrac{\cdots}{99}\) or \(\dfrac{3}{100} \times \dfrac{\cdots}{99}\) or \(\dfrac{15}{100} \times \dfrac{\cdots}{99}\) or \(\left(\dfrac{8}{100} \times \dfrac{\cdots}{99} + \dfrac{7}{100} \times \dfrac{\cdots}{99}\right)\)
(All correct)M1 3rd M1 for all correct
\(= \dfrac{87}{550}\) or \(0.158\) (3 sf)A1 
# Question 12:

| Answer/Working | Mark | Guidance |
|---|---|---|
| $P(\text{1st HGP}' \& \text{2nd GP}')$ or $(\text{1st HGP} \& \text{2nd GP}')$ or $(\text{1st HG}' \& \text{2nd GP}')$ | **M1** | One of the following expressions seen |
| $= \dfrac{25}{100} \times \dfrac{36}{99} + \dfrac{3}{100} \times \dfrac{37}{99} + \dfrac{15}{100} \times \dfrac{37}{99}$ | **M1** | Another expression seen: $\dfrac{25}{100} \times \dfrac{\cdots}{99}$ or $\dfrac{3}{100} \times \dfrac{\cdots}{99}$ or $\dfrac{15}{100} \times \dfrac{\cdots}{99}$ or $\left(\dfrac{8}{100} \times \dfrac{\cdots}{99} + \dfrac{7}{100} \times \dfrac{\cdots}{99}\right)$ |
| (All correct) | **M1** | 3rd M1 for all correct |
| $= \dfrac{87}{550}$ or $0.158$ (3 sf) | **A1** | |
12 The Venn diagram shows the numbers of students studying various subjects, in a year group of 100 students.\\
\includegraphics[max width=\textwidth, alt={}, center]{68f1107f-f188-4698-934e-8fd593b25418-7_554_910_347_244}

A student is chosen at random from the 100 students. Then another student is chosen from the remaining students.

Find the probability that the first student studies History and the second student studies Geography but not Psychology.

\section*{END OF QUESTION PAPER}
\section*{OCR}
Oxford Cambridge and RSA

\hfill \mbox{\textit{OCR PURE  Q12 [4]}}
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Q1 8 Q2 4 Q3 10 Q4 6 Q5 5 Q6 6 Q7 11 Q8 3 Q9 4 Q10 6 Q11 8 Q12 4