G5211 - Introduction to Probability - Events and their probabilities

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C N F Q I Y L J I S D E N S H T T B V L B
S D M U T U A L L Y E X C L U S I V E Q A
J K Q M B C D C L B O S P C B D I S L X R
F D M I U N P J P I Q T C G C L J M E N C
U E T H X A U W M Q V F L W X E X H F F O
A D D I T I O N L A W F V D N I Q V I S N
P E Y G I K X X I E I A A V I F A N X Q E
U Y O Y G A P E I V H P O R C A B O R J O
B N J I C L G A L F G J S F G M K B D F I
U F D C R C Y J W K A G W E O G V M M X U
G O S A M P L E S P A C E Y B I V V X J I
M H S T R O P E S J C U O K G S S G C P Q
L W F K E J M Q M Y F D D Q E P B O M M O
R T X C V N H O V U N P O S K K K O B V V
G K T K X G A N L F F U A X R V E N W F L
J R N S B B X K Y L E Q K W M T S D W M O
G R E E O L U K I N H C L S K R X N M V C
N D V P R O B A B I L I T Y S P A C E D A
R F E C M E G N J G T D S A C W D T F D K
U P W Q H Q A J U E M R B D W T P C P P P
T A Q G X J R A A T V U P L W D G C L M W

Clues

  • A collection of events is this if it satisfies the following properties: 1. the sample space is an element, 2. if A is an element then so is A composite, 3. if A,B,C are elements then so is AUBUCU... (5, 5)
  • For any finite collection of these type of events A,B,... P(union of events)=Sum of the probability of events. If they are this P(AUB)=P(A)+P(B) (8, 9)
  • It is a subset of the sample space. (5)
  • P(AUB) = P(A) + P(B) - P(AnB) (also known as the inclusion-exclusion principle) (8, 3)
  • The is the triple of sample space, the sigma field and all the events in the sigma field and must satifies the Probability axioms (11, 5)
  • The set of all possible outcomes of the experiment and is denoted by Ω (6, 5)

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