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Conditional Probability

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Question 122

A marine biologist analyzes 200 water samples from a local estuary for the presence of three specific pollutants: Nitrates (NNN), Phosphates (PPP), and Microplastics (MMM). The frequencies of these pollutants found in the samples are summarized as follows:

  • 110 samples contained none of the pollutants.
  • 18 samples contained only Nitrates.
  • 22 samples contained only Phosphates.
  • 14 samples contained only Microplastics.
  • 10 samples contained Nitrates and Phosphates, but not Microplastics.
  • 12 samples contained Nitrates and Microplastics, but not Phosphates.
  • 8 samples contained Phosphates and Microplastics, but not Nitrates.
  • 6 samples contained all three pollutants.

A sample is selected at random from the 200.

a.

Find the probability that the sample does not contain Microplastics.

[2]
b.

Find P(N∩P∩M′)P(N \cap P \cap M')P(N∩P∩M′).

[2]
c.

Find P(N∪P∪M′)P(N \cup P \cup M')P(N∪P∪M′).

[2]
d.

Find the probability that the sample contains at most one type of pollutant.

[2]
e.

Given the selected sample has at most one type of pollutant, find the probability it contains Nitrates.

[3]
f.

The random variable X X\,X is the number of the pollutants NNN, PPP, M M\,M found in a randomly selected sample.

Find E(X)E(X)E(X).

[3]

Conditional Probability Questions

  1. A Level
  2. /Maths
  3. /Conditional Probability

Practise Edexcel A Level Maths Conditional Probability with exam-style questions for A Level Maths. 152 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