Conditional Probabilities in Venn Diagrams

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Question 30

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

The frequencies for each category are distributed as follows:

Species that are ONLY migratory ( $M$ ): 12
Species that are ONLY water-dwelling ( $W$ ): 11
Species that are ONLY endangered ( $E$ ): 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 ( $\cap W \cap E$ ): 6
Species that possess none of these characteristics: 5

Describe in words the event $\cap E)$ .

[1]

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

[2]

Find $\cup W \cup E)')$ .

[2]

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

[2]

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

[2]

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

[2]

Conditional Probabilities in Venn Diagrams

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Question 30

The frequencies for each category are distributed as follows:

Species that are ONLY migratory ( $M$ ): 12
Species that are ONLY water-dwelling ( $W$ ): 11
Species that are ONLY endangered ( $E$ ): 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 ( $\cap W \cap E$ ): 6
Species that possess none of these characteristics: 5

Describe in words the event $\cap E)$ .

[1]

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

[2]

Find $\cup W \cup E)')$ .

[2]

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

[2]

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

[2]

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

[2]

Conditional Probabilities in Venn Diagrams

Question 30

Conditional Probabilities in Venn Diagrams Questions

Conditional Probabilities in Venn Diagrams

Question 30

Conditional Probabilities in Venn Diagrams Questions