STAT 400 Lecture AL1 Spring 2015 Dalpiaz Examples for 1 4 Events A and B are independent if and only if P B A P B P A B P A P A B P A P B 1 The probability that a randomly selected student at Anytown College owns a bicycle is 0 55 the probability that a student owns a car is 0 30 and the probability that a student owns both is 0 10 Are events a student owns a bicycle and a student owns a car independent Events A B and C are independent if and only if P A B P A P B P A C P A P C P B C P B P C and P A B C P A P B P C 2 A girl is told by her boyfriend that she is one in a billion She has a dimple in her chin probability 1 100 eyes of different colors probability 1 1 000 and is absolutely crazy about mathematics probability 1 10 000 a Do these events seem to be independent or dependent b Show why the girl is one in a billion 3 Bart and Nelson talked Milhouse into throwing water balloons at Principal Skinner Suppose that Bart hits his target with probability 0 80 Nelson misses 25 of the time and Milhouse hits the target half the time Assume that their attempts are independent of each other a Find the probability that all of them will hit Principal Skinner b Find the probability that exactly one of the boys will hit Principal Skinner c Find the probability that at least one of the boys will hit Principal Skinner Idea P at least one of A i occurs 1 P none of A i occurs P A 1 or A 2 or or A n 1 P not A 1 and not A 2 and and not A n P A 1 A 2 A n 1 P A 1 A 2 A n For independent events P A 1 or A 2 or or A n 1 P not A 1 P not A 2 P not A n P A 1 A 2 A n 1 P A 1 P A 2 P A n 4 Often On time Parcel Service OOPS delivers a package to the wrong address with probability 0 05 on any delivery Suppose that each delivery is independent of all the others There were 7 packages delivered on a particular day What is the probability that at least one of them was delivered to the wrong address 5 A major oil company has decided to drill independent test wells in the Alaskan wilderness The probability of any well producing oil is 0 30 Find the probability that the fifth well is the first to produce oil 6 An automobile salesman thinks that the probability of making a sale is 0 30 If he talks to five customers on a particular day what is the probability that he will make exactly 2 sales Assume independence Series Connection Reliability r1 r2 In general r1 r2 rk Parallel Connection Reliability 1 1 r 1 1 r 2 r1 In general 7 r2 r1 r2 1 1 r 1 1 r 2 1 r k Compute the reliability of the following system of independent components the numbers represent the reliability of each component
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