Transcription of Sample Space, Events and Probability
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Sample Space, Events and Probability
Sample Space, Events and ProbabilitySample Space and EventsThere are lots of phenomena in nature, like tossing a coin or tossing a die, whose outcomescannot be predicted with certainty in advance, but the set of all the possible outcomes is are what we callrandom phenomenaorrandom experiments. Probability theory is concernedwith such random phenomena or random a random experiment. The set of all the possible outcomes is called thesample spaceof the experiment and is usually denoted byS. Any subsetEof the Sample spaceSis called anevent. Here are some 1 Tossing a coin. The Sample space isS={H, T}.E={H}is an 2 Tossing a die.
(v) For any events E and F, P(E [F) = P(E)+P(F) P(E \F). (vi) For any n 2 and any events E 1;:::;E n, P([n i=1E i) = Xn i=1 P(E i) X i 1<i 2 P(E i 1 \E i 2)+ +( 1) k+1 X i 1< <i k P(\k j=1E i j)+ +( 1) n+1P(\n i=1E i): The last formula is called the inclusion-exclusion formula. Proof. We are only going to prove (i), (ii), (v). (vi) follows from ...
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