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2.3 Conditional Probabilities in Venn Diagrams

2.3 Conditional Probabilities in Venn Diagrams

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Question 25

In a reliability study of a satellite system, the events A A\,A and B B\,B represent the satellite experiencing a thermal fluctuation and a signal transmission delay respectively. It is known that

P(A)=0.3P(A∪B)=0.58 P(A) = 0.3 \quad P(A \cup B) = 0.58 P(A)=0.3P(A∪B)=0.58

Given that A A\,A and B B\,B are independent,

a.

show that P(B)=0.4P(B) = 0.4P(B)=0.4

(4)

[4]
b.

The event C C\,C represents a specific sensor failure that is known to occur only during thermal fluctuations, such that

P(C)=0.12P(A∩C)=P(C) P(C) = 0.12 \quad P(A \cap C) = P(C) P(C)=0.12P(A∩C)=P(C)

Find P(C′∣A)P(C' | A)P(C′∣A)

(2)

[2]
c.

Given that B B\,B and C C\,C are mutually exclusive,

draw a Venn diagram to represent the events AAA, B B\,B and CCC, giving the exact probabilities of each region in the Venn diagram.

(5)

[5]
Markscheme

2.3 Conditional Probabilities in Venn Diagrams Questions

  1. A Level
  2. /Maths
  3. /2.3 Conditional Probabilities in Venn Diagrams

31 exam-style questions on Edexcel A Level Maths 2.3 Conditional Probabilities in Venn Diagrams. Each one has a worked solution and a mark scheme showing where the marks go.

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