AS LEVEL MATHS STATS PROBABILITY, Exercises of Mathematics

AS LEVEL MATHS STATS PROBABILITY

Typology: Exercises

2025/2026

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PROBABILITY
Applied Year 1, Chapter 5
Venn diagrams
Venn diagrams
Regions can be filled with
frequencies or probabilities
โ€˜Orโ€™, union, ๐‘จ โˆช ๐‘ฉ
Shade all of ๐ด, shade all of ๐ต
โ€˜Andโ€™, intersection ๐‘จ โˆฉ ๐‘ฉ
Lightly shade all of ๐ด, lightly
shade all of ๐ต โ€“ for final
shading, only shade their
overlap
โ€˜Notโ€™, complement, ๐‘จโ€ฒ
Consider ๐ด, then shade
everything outside this area
Correctly shade the following Venn diagrams:
(Year 1, no conditional probability)
๐ด๐ต๐ด๐ต
๐ถ
๐ด๐ต
๐ถ
๐ด๐ต
๐ถ
๐ด โˆช ๐ตโ€ฒ (๐ด โˆฉ ๐ถ) โˆช ๐ต
๐ด โˆฉ ๐ตโ€ฒ โˆฉ ๐ถ ๐ด โˆฉ ๐ตโ€ฒ โˆฉ๐ถโ€ฒ
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PROBABILITY

Applied Year 1, Chapter 5

Venn diagrams

Venn diagrams Regions can be filled with frequencies or probabilities โ€˜Orโ€™, union, ๐‘จ โˆช ๐‘ฉ Shade all of ๐ด, shade all of ๐ต โ€˜Andโ€™, intersection ๐‘จ โˆฉ ๐‘ฉ Lightly shade all of ๐ด, lightly shade all of ๐ต โ€“ for final shading, only shade their overlap โ€˜Notโ€™, complement, ๐‘จโ€ฒ Consider ๐ด, then shade everything outside this area Correctly shade the following Venn diagrams:

(Year 1, no conditional probability)

Independent events, mutually exclusive events Independent events The outcome of one event has no effect on the outcome of the other event Events are independent if: ๐‘ƒ ๐ด โˆฉ ๐ต = ๐‘ƒ(๐ด) ร— ๐‘ƒ(๐ต) You cannot easily tell if events are independent by looking at the Venn diagram Mutually exclusive events Events which cannot both occur simultaneously Shown on a Venn diagram by events which do not overlap ๐‘ƒ ๐ด โˆช ๐ต = ๐‘ƒ ๐ด + ๐‘ƒ(๐ต)

  1. (^24 0). 3 ๐‘ ๐‘ž ๐‘Ÿ The Venn diagram, where ๐‘, ๐‘ž and ๐‘Ÿ are probabilities, shows the 3 events ๐ด, ๐ต and ๐ถ with their associated probabilities. a) Write down the pair of mutually exclusive events b) Given that ๐ด and ๐ต are independent, and that ๐‘ƒ ๐ต = 2๐‘ƒ(๐ถ), find the values of ๐‘, ๐‘ž and ๐‘Ÿ c) Write down ๐‘ƒ(๐ด โˆฉ ๐ต โˆฉ ๐ถ)