handout240.6 - Handout 6. Probability 4.5-4.6 Probability...

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1 Handout 6. Probability 4.5-4.6 Probability Concepts: Mutually Exclusive Events – If A occurs, then B cannot occur – A and B have no common elements Black Cards Red Cards A card cannot be Black and Red at the same time. A B Independent and Dependent Events Independent: Occurrence of one does not influence the probability of occurrence of the other Dependent: Occurrence of one affects the probability of the other Independent Events A = heads on one flip of a fair coin B = heads on second flip of same coin Result of second flip does not depend on the result of the first flip. Dependent Events A = rain forecasted on the news B = take umbrella to work Probability of the second event is affected by the occurrence of the first event. Conditional Probability Example 6.1 No CD CD Total AC .2 .5 .7 No AC .2 .1 .3 Total .4 .6 1.0 • Of the cars on a used car lot, 70% have air conditioning (AC) and 40% have a CD player (CD). 20% of the cars have both. What is the probability that a car has a CD player, given that it has AC ? i.e., we want to find P(CD | AC) .2857 .7 .2 P(AC) AC) and P(CD AC) | P(CD = = = Given AC, we only consider the top row (70% of the cars). Of these, 20% have a CD player. 20% of 70% is about 28.57%.What is the probability that the car has air conditioning , given that it has CD? Conditional Probabilities The probability that A occurs, given that event B has occurred is called the conditional probability of A given B and is defined as Think about events A and B spaced in time (B has occured). 0 ) ( if ) ( ) ( ) | ( = B P B P AB P B A P “given”
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2 Multiplication law: P(AB)=P(B)P(A|B) or P(AB)=P(A)P(B|A) Two events A and B are independent when (1) P(A|B)=P(A). That is, the probability that A occurs does not change with the occurrence of B, or (2) P(B|A)=P(B)
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handout240.6 - Handout 6. Probability 4.5-4.6 Probability...

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