Summary of Key Definitions

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Summary of Key Definitions
It is important to understand the differences between complement, mutually exclusive, intersection, independent, and union!


"Complement"
P(A)+P(Ac)=1P(A)+P(A^c)=1P(A)+P(Ac)=1

  
The probability of Event A and the probability of Event not-A add up to 100%.

"Mutually Exclusive" (or Disjoint)
P(A∩B)=0P(A\cap B)=0P(A∩B)=0

  
Event A and Event B do not overlap.

"Intersection"
P(A∩B)P(A\cap B)P(A∩B)

  

Event A and Event B overlap. Intersection is the opposite of mutually exclusive.

"Independent"
P(A)⋅P(B)=P(A∩B)P(A)\cdot P(B)=P(A\cap B)P(A)⋅P(B)=P(A∩B)

  

The occurrence of Event A does not affect the occurrence of Event B, and vice versa.

"Union"
P(A∪B)=P(A)+P(B)−P(A∩B)P(A\cup B)=P(A)+P(B)-P(A\cap B)P(A∪B)=P(A)+P(B)−P(A∩B)

  

When Event A and Event B overlap, you need to subtract the overlap portion to avoid double-counting.

Wize University Statistics Textbook > Probability

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Summary of Key Definitions