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2.3 Probability

2.3 Probability

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Question 150

A research study analyzed 150 local councils to determine which wildfire prevention strategies they implemented. The strategies monitored were Prescribed Burns (BBB), Firebreaks (FFF), and Vegetation Management (VVV). The findings were as follows:

  • 85 councils implemented Prescribed Burns (BBB)
  • 70 councils implemented Firebreaks (FFF)
  • 75 councils implemented Vegetation Management (VVV)
  • 48 implemented both Prescribed Burns and Firebreaks
  • 38 implemented both Firebreaks and Vegetation Management
  • 42 implemented both Prescribed Burns and Vegetation Management
  • 25 implemented all three strategies
a.

Draw a Venn Diagram to represent these data.

[3]
b.

Find the probability that a randomly selected council from the study:

implemented none of these strategies,

[1]
c.

Find the probability that a randomly selected council from the study:

implemented Firebreaks but did not implement Prescribed Burns,

[2]
d.

Find the probability that a randomly selected council from the study:

implemented at least two of these strategies.

[2]
e.

A specific council, RedLeaf, is known to have implemented Prescribed Burns.

Find the probability that RedLeaf implemented Firebreaks but did not implement Vegetation Management.

[2]
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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