204 5.2%2c5.3%2c5.4 Properties of Probability

204 5.2%2c5.3%2c5.4 Properties of Probability - valid for...

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5.2 Properties of Probability Compliments and The Addition Rule From the above definitions we can quickly develop a few properties of probability . For example, the probability of an event (E) can be no less than 0(it never occurs) and no more than 1 ( it always occurs) 0 P(E) 1 Also (probability of E occurring)+(probability of E not occurring)= 1 P(E) + P( not E) = 1 Addition Rule Mutually Exclusive Events If a sequence events (E 1 , E 2, E 3 , . . . E n ) are mutually exclusive the probability of their union is: P(E 1 or E 2 or E 3 , … or E n ) = P(E 1 ) + P(E 2 ) + . .. + P(E n ) Example: Assume you randomly take a ball from a container that contains 3 red balls, 5 blue balls, 8 yellow balls, and 2 orange balls (total = 18 balls); what is the probability of a red or orange ball if one ball is randomly selected. P(red or orange) = 3/18 + 2/18 = 5/18 General “Addition” Rule for the union of events (i.e. it is
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Unformatted text preview: valid for mutually exclusive or non-exclusive events) P(A or B) = P(A) + P(B) - P(A and B) A C B 5.3 Multiplication Rule For Independent Events If E 1 , E 2, E 3 , . . . E n independent events, the probability of their intersection is: P(E 1 and E 2 and E 3 , … and E n ) = P(E 1 ) * P(E 2 ) * . .. * P(E n ) Example1: Roll a die and select a card from a deck of 52 cards. Specifically, find the probability of rolling a 4 and selecting a club = P(4)*p(club) = 1/6 * 1/4 = 1/24 Example 2 5.4 General “Multiplication” Rule and Conditional Probability for the intersection of events Note: P(A|B) = the probability of A given that B has occurred The probability of A given B is: P(A|B) = P(AB)/P(B) The probability of B given A is: P(B|A) = P(AB)/P(A) Thus the probability of A and B is: P(AB) = P(A|B)P(B) = P(B|A)P(A) B A A C B...
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This note was uploaded on 12/05/2011 for the course MATH 2040 taught by Professor Raysievers during the Fall '10 term at Utah Valley University.

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204 5.2%2c5.3%2c5.4 Properties of Probability - valid for...

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