Function : A function is a mapping in which every element in one set is mapped to exactly one element of a second set. Most often the mapping is described using a rule. For example the function $f(x)=x+1$ maps 2 to 3 and -1 to 0.

Bayes' theorem : Bayes theorem is the following formula for conditional probabilities that states how to update the probability $P[A]$ to take into account evidence $B$ for $A.$: $P[A|B]=\frac{P[B|A]\cdot P[A]}{P[B]}$ $=\frac{P[B|A]\cdot P[A]}{P[B|A]\cdot P[A]+P[B|\neg A]\cdot P[\neg A]}.$

Half : A Half is the number equal to $\frac{1}{2}=0.5.$

Positive : Positive means $\geq 0.$

Probability : A probability is a number between 0 and 1 that describes how likely an outcome is. For discrete events that are equally likely the probability can be calculated by dividing the number of favorable outcomes by the number of possible outcomes.

Random experiment : A random experiment is an experiment in which the result can not be foreseen with certainty.

Cubed : The cube of a number $x$, or $x$ cubed or $x^3$ is the third power of $x$: $x^3=x\cdot x\cdot x.$ For example 2 cubed equals 8.

Induction : Induction is a common techniques for proofing mathematical results that are dependent on a natural number $n.$ It consists of first proving the result for a specific $n$, often $n=0$ or $n=1$ (the induction base) and then proving that if it the results holds for all numbers smaller than $n$ that it will then also hold true for $n$ (the induction step.)

Number : A number $x$ is a mathematical symbol representing a quantity.

Polynomial expansion : Polynomial expansion refers to multiplying out brackets in a factorization of a polynomial. The most commonly used polynomial expansions are $(x+y)^2=x^2+2xy+y^2,$ $(x-y)^2=x^2-2xy+y^2$ and $(x+y)(x-y)=x^2-y^2.$

Squared : $x$ squared refers to the number $x^2=x\cdot x.$ For example 3 squared equals 9.

Sum : A sum is the result of an addition.