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Conditional Probability

Conditional Probability

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Question 283

A botanical research station analyzes 50 plant samples for the presence of three specific enzymes: Alpha (AAA), Beta (BBB), and Gamma (ΓΓΓ). The distribution of these enzymes across the samples is summarized in the following data:

  • 9 samples contain only enzyme AAA.
  • 6 samples contain both enzymes A A\,A and BBB, but not ΓΓΓ.
  • 11 samples contain only enzyme BBB.
  • 4 samples contain both enzymes B B\,B and ΓΓΓ, but not AAA.
  • 8 samples contain only enzyme ΓΓΓ.
  • 12 samples contain none of these enzymes.
  • No samples contain both A A\,A and Γ Γ\,Γ simultaneously.

One sample is selected at random.

a.

Show that the probability that the sample contains more than one enzyme is 0.2.

[2]
b.

Determine the probability that the sample contains enzyme A A\,A or enzyme BBB (or both).

[2]
c.

State the probability that the sample contains both enzyme A A\,A and enzyme ΓΓΓ.

[1]
d.

Given that the sample is found to contain at least one of the three enzymes,

calculate the probability that it contains enzyme ΓΓΓ.

[3]
e.

Determine, with a reason, whether the presence of enzyme B B\,B and the presence of enzyme Γ Γ\,Γ in a sample are statistically independent events.

[4]
Markscheme

Conditional Probability Questions

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

368 exam-style questions on Edexcel A Level Maths Conditional Probability, covering 2.1 Set Notation, 2.2 Conditional Probability, 2.3 Conditional Probabilities in Venn Diagrams, 2.4 Probability Formulae, and 2.5 Tree Diagrams. Each one has a worked solution and a mark scheme showing where the marks go.

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