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Conditional Probability

Conditional Probability

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Question 324

A ecological survey identifies 60 distinct bird species inhabiting a forest reserve. The species are categorized by three characteristics: being migratory (MMM), being water-dwelling (WWW), and being endangered (EEE).

The frequencies for each category are distributed as follows:

  • Species that are ONLY migratory (MMM): 12
  • Species that are ONLY water-dwelling (WWW): 11
  • Species that are ONLY endangered (EEE): 14
  • Species that are both migratory and water-dwelling, but NOT endangered: 3
  • Species that are both migratory and endangered, but NOT water-dwelling: 4
  • Species that are both water-dwelling and endangered, but NOT migratory: 5
  • Species that possess all three characteristics (M∩W∩EM \cap W \cap EM∩W∩E): 6
  • Species that possess none of these characteristics: 5
a.

Describe in words the event (W∩E)(W \cap E)(W∩E).

[1]
b.

Write down the probability that a species selected at random is migratory.

[2]
c.

Find P((M∪W∪E)′)P((M \cup W \cup E)')P((M∪W∪E)′).

[2]
d.

Given that the species selected is endangered: find the probability that it is migratory.

[2]
e.

State, with a reason, whether or not the events M M\,M and E E\,E are statistically independent.

[2]
f.

Given that the species selected is both water-dwelling and endangered: find the probability that it is migratory.

[2]
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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