Determine whether you think the given pair of events is independent. You frequent casinos. You have lost...

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Determine whether you think the given pair of events isindependent.
You frequent casinos. You have lost money gambling.

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mutually exclusive are independent their intersection isemptyWhen we were working out the probability of the ball landing ina black or red pocket we were dealing with two separate eventsthe ball landing in a black pocket and the ball landing in a redpocket These two events are mutually exclusive becauseits impossible for the ball to land in a pocket thats both blackand redIf two eventsare mutually exclusive only one of the two can occurWhat about the black and even events This time the eventsarent mutually exclusive Its possible that the ball could landin a pocket thats both black andeven The two eventsintersectIf two eventsintersect its possible they can occursimultaneouslyBRAIN POWERWhat sort of effect do you think this intersection could havehad on the probabilityProblems at the intersectionCalculating the probability of getting a black or even wentwrong because we included black and even pockets twice Heres whathappenedFirst of all we found the probability of getting a black pocketand the probability of getting an even numberWhen we added the two probabilities together we counted theprobability of getting a black and even pocket twiceTo get the correct answer we need to subtract the probabilityof getting both black and even This gives usPBlack or Even PBlack PEven PBlack andEvenWe can now substitute in the values we just calculated to findPBlack or EvenPBlack or Even 1838 1838 1038 2638 0684Some more notationTheres a more general way of writing this using some more mathshorthandFirst of all we can use the notation A B to refer to theintersection between A and B You can think of this symbol asmeaning and It takes the common elements of eventsA B on the other hand means the union of A and B Itincludes all of the elements in A and also those in B You canthink of it as meaning orIf A B 1 then A and B are said to be exhaustiveBetween them they make up the whole of S They exhaust allpossibilitiesSHARPEN YOUR PENCILOn the previous page we found thatPBlack or Even PBlack PEven PBlack and EvenWrite this equation for A and B using and notationSHARPEN YOUR PENCIL SOLUTIONOn the previous page we found thatPBlack or Even PBlack PEven PBlack and EvenWrite this equation for A and B using and notationPA B PA PB PA BNOTEPA or BPA and BIts not actually that differentMutually exclusive events have no elements in common with eachother If you have two mutually exclusive events the probabilityof getting A and B is actually 0so PA B 0 Lets revisit ourblackorred example In this bet getting a red pocket on theroulette wheel and getting a black pocket are mutually exclusiveevents as a pocket cant be both red and black This means thatPBlack Red 0 so that part of the equation justdisappearsWATCH ITTheres a difference between exclusive andexhaustiveIf events A and B are exclusive thenPA B 0If events A and B are exhaustive thenPA B 1BE THE See Answer

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