Probability

A measure of the likelihood of an event occurring
$P (A)$ is the probability of A occurring
Theoretical Probability: theory probability, e.g. 50% chance of getting a tails in a coin flip $\frac{P ( A )}{n u mb er o f p oss ib l e res u lt s}$
Experimental Probability: Probability from results, e.g. from the results, you might only get a tails 48 times out of 100. See relative frequency.

Notation	Meaning
A	Set of elements in A
U	Universal set - all elements in consideration
A’ or $\overline{A}$	Complement of A - Elements not in A
A $\cap$ B	Intersection of A and B - elements in both A and B
A $\cup$ B	Union of A and B - elements in A or B (or both)
n(A)	Number of elements in A
$\emptyset$	Empty set

P(B|A) is the probability of B given A has occurred $P (B ∣ A) = \frac{P ( B \cap A )}{P ( A )}$
Relative frequency of A: $\frac{n u mb er o f t r ia l s A occ u rs}{n u mb er o f t r ia l s co n d u c t e d} \approx P (A)$
Independence Test; An event is independent if: $P (A \cap B) = P (A) \times P (B)$ $P (A ∣ B) = P (A)$
Mutually Exclusive Events: 2 events are mutually exclusive (can’t occur at the same time) if: $P(A\cup B)=P(A)+P(B)$$$$P(A \cap B)=0$
Multiplication Rule: $P (A \cap B) = P (A) \times P (B ∣ A)$
Addition Rule $P (A \cup B) = P (A) + P (B) - P (A \cap B)$ $P (A \cap B) = P (A) + P (B) - P (A \cup B)$

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