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2.3 Probability

2.3 Probability

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Question 137

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]
Markscheme

2.3 Probability Questions

  1. A Level
  2. /Maths
  3. /2.3 Probability

200 exam-style questions on OCR (MEI) A Level Maths 2.3 Probability, covering 2.3.1 Calculate the probability of an event, 2.3.2 Complementary events, 2.3.3 Expected frequency of an event, 2.3.4 Diagrams to calculate probabilities, 2.3.5 Mutually exclusive and independent events, 2.3.6 Add probabilities for mutually exclusive events, 2.3.7 Multiply probabilities for independent events, 2.3.8 Mutually exclusive and independent events (notation) (A-level only), 2.3.9 Venn diagrams for probabilities (A-level only), 2.3.10 Conditional probabilities (A-level only), and 2.3.11 Independence via conditional probability (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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