, Definitions
Outcome
A single observation/realisation of a random process.
Sample Space
A set of all possible outcomes of an experiment.
Event
Any subset of a sample space.
Union (𝑨𝑨 ∪ 𝑩𝑩)
The set of outcomes that belong to at least one of A or B, or
both.
Intersection (𝑨𝑨 ∩ 𝑩𝑩)
The set of all possible outcomes that belong to both A and B.
Complement (𝑨𝑨𝒄𝒄 )
The 𝐴𝐴𝑐𝑐 of an event A is the set of all outcomes that are not in A.
Mutually Exclusive (𝑷𝑷(𝑨𝑨 ∩ 𝑩𝑩) = 𝟎𝟎)
A and B are said to be this if they have no outcomes in
common i.e., if A and B cannot occur together.
, Probability (𝑷𝑷(𝑨𝑨))
The proportion/fraction of times that a particular event
would occur in a long run of observations.
Order of Magnitude
The smallest power of 10 required to represent a number 𝑎𝑎 in
the form 𝑎𝑎 × 10𝑏𝑏 , where 𝑏𝑏 is the Order of Magnitude.
Area of a Sphere: 𝐴𝐴 = 4𝜋𝜋𝑟𝑟 2
𝑎𝑎+𝑏𝑏
Area of a Trapezoid: 𝐴𝐴 = ℎ
2
𝑙𝑙𝑙𝑙ℎ
Volume of a Pyramid with Rectangular Base: 𝑉𝑉 = 3
Outcome
A single observation/realisation of a random process.
Sample Space
A set of all possible outcomes of an experiment.
Event
Any subset of a sample space.
Union (𝑨𝑨 ∪ 𝑩𝑩)
The set of outcomes that belong to at least one of A or B, or
both.
Intersection (𝑨𝑨 ∩ 𝑩𝑩)
The set of all possible outcomes that belong to both A and B.
Complement (𝑨𝑨𝒄𝒄 )
The 𝐴𝐴𝑐𝑐 of an event A is the set of all outcomes that are not in A.
Mutually Exclusive (𝑷𝑷(𝑨𝑨 ∩ 𝑩𝑩) = 𝟎𝟎)
A and B are said to be this if they have no outcomes in
common i.e., if A and B cannot occur together.
, Probability (𝑷𝑷(𝑨𝑨))
The proportion/fraction of times that a particular event
would occur in a long run of observations.
Order of Magnitude
The smallest power of 10 required to represent a number 𝑎𝑎 in
the form 𝑎𝑎 × 10𝑏𝑏 , where 𝑏𝑏 is the Order of Magnitude.
Area of a Sphere: 𝐴𝐴 = 4𝜋𝜋𝑟𝑟 2
𝑎𝑎+𝑏𝑏
Area of a Trapezoid: 𝐴𝐴 = ℎ
2
𝑙𝑙𝑙𝑙ℎ
Volume of a Pyramid with Rectangular Base: 𝑉𝑉 = 3
