A-Level Mathematics: Conditional Probabilities in Venn Diagrams questions

Q: A region in a Venn diagram has P(A)=0.6, P(B)=0.5, and P(A B)=0.2. What is P(A B)?

B1: Uses P(A B)= P(A B)P(B)= 0.20.5=0.4. Accept: 0.4 or 25. Do not award: uses P(A) instead of P(B) in the denominator; gives 0.2 or 0.3 from incorrect division.

Q: In a class, 60 students study French, 45 study German and 20 study both French and German. A student is chosen at random from those who study French. What is the probability that the student also studies German?

M1: Uses conditional probability as P(G F)= P(G F)P(F) or equivalent count ratio 2060. 1: 13. 20/60, 1/3. not award for 2045, 4560, or using the total number of students as the denominator.

Q: In a survey, 40 students study Physics, 28 study Chemistry, and 12 study both subjects. A student is chosen at random from those who study Physics or Chemistry. Find the probability that the student studies Chemistry given that the student studies Physics or Chemistry. Give your answer as a fraction

M1: Finds the number in P C as 40+28-12=56. M1: Uses conditional probability P(C P C)= P(C (P C))P(P C) or equivalent reasoning, giving 2856. A1: 12? No: do not award this; correct answer is 717. A1: 717. Accept 1434 before simplification. Do not award for dividing by 40, 28, or 12 alone, or for using P(C P)= 1240.

4 exam-style questions on conditional probabilities in venn diagrams, each with a full mark scheme. Written for Edexcel. These are Kepler’s own questions, not reproduced past papers.

Question 11 mark

A region in a Venn diagram has $P(A)=0.6$ , $P(B)=0.5$ , and $P(A\cap B)=0.2$ . What is $P(A\mid B)$ ?

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B1: Uses $P(A\mid B)=$ \frac{P(A\cap B)}{P(B)} $=$ \frac{0.2}{0.5} $=0.4$ . Accept: $0.4$ or $\frac{2}{5}$ . Do not award: uses $P(A)$ instead of $P(B)$ in the denominator; gives $0.2$ or $0.3$ from incorrect division.

Question 21 mark

In a class, $60$ students study French, $45$ study German and $20$ study both French and German. A student is chosen at random from those who study French. What is the probability that the student also studies German?

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M1: Uses conditional probability as $P(G\mid F)=\frac{P(G\cap F)}{P(F)}$ or equivalent count ratio $\frac{20}{60}$ .\nA1: $\frac{1}{3}$ .\nAccept $20/60$ , $1/3$ .\nDo not award for $\frac{20}{45}$ , $\frac{45}{60}$ , or using the total number of students as the denominator.

Question 33 marks

In a survey, 40 students study Physics, 28 study Chemistry, and 12 study both subjects. A student is chosen at random from those who study Physics or Chemistry. Find the probability that the student studies Chemistry given that the student studies Physics or Chemistry. Give your answer as a fraction in its simplest form.

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M1: Finds the number in $P \cup C$ as $40+28-12=56$ . M1: Uses conditional probability $P(C\mid P\cup C)=\frac{P(C\cap(P\cup C))}{P(P\cup C)}$ or equivalent reasoning, giving $\frac{28}{56}$ . A1: $\frac{1}{2}$ ? No: do not award this; correct answer is $\frac{7}{17}$ . A1: $\frac{7}{17}$ . Accept $\frac{14}{34}$ before simplification. Do not award for dividing by 40, 28, or 12 alone, or for using $P(C\mid P)=\frac{12}{40}$ .

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A-Level Mathematics: Conditional Probabilities in Venn Diagrams questions

4 exam-style questions on conditional probabilities in venn diagrams, each with a full mark scheme. Written for Edexcel. These are Kepler’s own questions, not reproduced past papers.

Question 11 mark

A region in a Venn diagram has $P(A)=0.6$ , $P(B)=0.5$ , and $P(A\cap B)=0.2$ . What is $P(A\mid B)$ ?

Show the mark scheme

Question 21 mark

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Question 33 marks

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