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2.3 Probability

2.3 Probability

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Question 109

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

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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