Basic probability Sample Space (S): set of all outcomes of an experiment Event (E): any collection of outcomes Probability of an event E, written as P(E)

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Presentation transcript:

Basic probability Sample Space (S): set of all outcomes of an experiment Event (E): any collection of outcomes Probability of an event E, written as P(E) = The fraction of times the event E occurs out of large number trials

Properties 1. 0≤P(E)≤1 for any event, E. 2. P(E)=1 if E is certain to occur. 3.P(E  F)=P(E) + P(F), If both E and F cannot happen at the same time. 4. P(S) = 1, if S is sample space

More properties For any Events E and F, 1. P(EF) = P(E) + P(F) – P(EF) 2. P(E C ) = 1- P(E) 3. P(E C F C ) = P((EF) C ) = 1-P(EF) 4. P(E C F C ) = P((EF) C ) = 1-P(EF)

Important notation usage Let S be a sample space. For any events A and B, A or B means AB ( In A or in B or both) A and B means AB ( Common in A and B) A does not occur means A C ( Not in A)

Correct usage of Notation Correct AB=S P(A C )= 1- P(A) P(A) + P(B) =.4 P({}) = 0 or P()=0 Not correct A + B = S A C = 1 – A A + B =.4 {} = 0 or  = 0

Correct Mathematical expressions for the given statements Let S be a sample space. For any events E and F, 1. Probability that either E or F occurs = P(E  F) 2. Probability that Neither E nor F occurs = P(E C  F C) 3. Probability that exactly one event occurs = P(E C F)+ P(EF C ) = [P(F)-P(EF)]+ [P(E)-P(EF)]