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2.3 Probability

2.3 Probability

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Question 157

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

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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