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2.3 Conditional Probabilities in Venn Diagrams

2.3 Conditional Probabilities in Venn Diagrams

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Question 21

An automated manufacturing system monitors three specific types of production errors: Event DDD (calibration drift), Event SSS (sensor saturation), and Event MMM (mechanical misalignment).

The probabilities of these errors occurring in a single cycle are given by:

P(D)=0.3,P(S∣D)=0.4,P(D∪S)=0.58,P(M)=0.5 P(D) = 0.3, \quad P(S|D) = 0.4, \quad P(D \cup S) = 0.58, \quad P(M) = 0.5 P(D)=0.3,P(S∣D)=0.4,P(D∪S)=0.58,P(M)=0.5

Events DDD and MMM are known to be mutually exclusive.

a.

Find P(D∪M)P(D \cup M)P(D∪M).

[2]
b.

Show that P(S)=0.4P(S) = 0.4P(S)=0.4.

[3]
c.

Given also that events SSS and MMM are independent,

draw a Venn diagram to represent the events DDD, SSS and MMM, indicating the probability associated with each of the eight regions.

[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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