2201 Prelim 1 Review - Probability: A number between 0 and...

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Unformatted text preview: Probability: A number between 0 and 1 that denotes the likelihood an event occurs  If P(E) = 1, then E contains all possible outcomes  Also known as sample space  If P(E) = 0, then E contains no possible outcomes  Also known as null set P(E) = (n e /n) as n approaches infinite  Number of times that the event E occurs over the total number of repetitions of the experiment If I flipped a coin 300 times, and received 150 heads, then P(heads) = 150/300 = .5 P(E) = N e /N s  The probability is equal to the number of outcomes in event E, divided by the total possible outcomes  Only when each outcome is equally likely to occur I flipped a coin 3 times, whats the probability that exactly 2 of them are heads? First list what the event is:  E = {2 of 3 are heads} =  {HTH, HHT, THH}  Then list all the possible outcomes  S = {TTT, TTH, THH, THT, HHH, HHT, HTT, HTH} So the probability that exactly 2 are heads is P(E) = E/S, = 3/8 Independent : Two events are considered independent if the occurrence of one does not influence the occurrence of the other.  Tossing a coin and talking, no effect on each other  Mutually Exclusive : Two events are considered mutually exclusive if they cannot both happen at the same time, one or the other  Standing and Sitting down Intersection  E F : E intersect F, is the event that contains the outcomes of both E and F E F E F Intersection of the sets {1,2,3} and {2,3,4}  {2,3}  If and only if E & F are independent then the Probability of the intersection is the product of the probabilities  P(E) = .5 If E and F are independent, P(E F) =  P(F) = .4 P(E)*P(F) = (.5)*(.4) = .2 Union ...
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This note was uploaded on 04/28/2010 for the course HADM 2236 taught by Professor Spies during the Spring '09 term at Cornell University (Engineering School).

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2201 Prelim 1 Review - Probability: A number between 0 and...

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