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Conditional Probabilities in Venn Diagrams

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Question 29

The Venn diagram illustrates the specialized competencies of 40 researchers in a data science lab. The events are defined as:

PPP: Researcher is proficient in Python

SSS: Researcher is proficient in SQL

BBB: Researcher is proficient in Bioinformatics

Within the universal set of 40 researchers:

  • The number who are proficient in Python only is 11.
  • The number proficient in both Python and SQL is 9.
  • The number proficient in SQL only is 10.
  • The number proficient in Bioinformatics (which has no overlap with Python or SQL) is 8.
  • The number with none of these proficiencies is 2.

Venn diagram for 40 researchers, with overlapping sets P and S and a separate set B.

a.

Identify two of these events that are mutually exclusive. Justify your answer.

[2]
b.

Determine whether or not the events PPP and SSS are independent.

[3]
c.

One researcher is selected at random. Calculate the probability that this person:

is proficient in Bioinformatics,

[1]
d.

is proficient in both Python and SQL.

[1]
e.

Given that this researcher is proficient in Python, find the probability that they are also proficient in SQL.

[2]

Conditional Probabilities in Venn Diagrams Questions

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

Practise Edexcel A Level Maths Conditional Probabilities in Venn Diagrams with exam-style questions for A Level Maths. 32 questions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.

Question bank