STAT 400 Lecture AL1 Spring 2015 Dalpiaz Answers for 1 3 The conditional probability of A given B the probability of event A computed on the assumption that event B has happened is P A B P A B P B assuming P B 0 Similarly the conditional probability of B given A is P A B P B A P A 3 assuming P A 0 C C B 0 10 0 45 0 55 B 0 20 0 25 0 45 0 30 0 70 1 00 continued 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 P B 0 55 P C 0 30 P B C 0 10 a What is the probability that a student owns a bicycle given that he she owns a car P B C 0 10 0 30 1 3 b Suppose a student does not have a bicycle What is the probability that he she has a car P C B 0 20 0 45 4 9 5 continued Suppose P A 0 22 P B 0 25 P C 0 28 P A B 0 11 P A C 0 05 P B C 0 07 P A B C 0 01 Find the following a P B A P B A 0 11 0 22 0 50 b P B C c P B C A 0 01 0 22 1 22 P B C 0 07 0 28 0 25 d P B C A e P B C A 0 15 0 22 15 22 f P C A B g P C A B 0 01 0 11 1 11 P C A B 0 11 0 36 11 36 P C A B P B C A P A B C A B C P A B C A B C 0 01 0 53 1 53 Multiplication Law of Probability If A and B are any two events then P A B P A P B A P A B P B P A B 8 It is known that 30 of all the students at Anytown College live off campus Suppose also that 48 of all the students are females Of the female students 25 live off campus P Off 0 30 a P F 0 48 P Off F 0 25 What is the probability that a randomly selected student is a female and lives off campus P F Off P F P Off F 0 48 0 25 0 12 b Off On F 0 12 0 36 0 48 M 0 18 0 34 0 52 0 30 0 70 1 00 What is the probability that a randomly selected student either is a female or lives off campus or both P F Off P F P Off P F Off 0 48 0 30 0 12 0 66 OR P F Off P F Off P F Off P F Off 0 12 0 18 0 36 0 66 OR P F Off 1 P F Off 1 0 34 0 66 c What proportion of the off campus students are females P F Off 0 12 0 30 0 40 d What proportion of the male students live off campus P Off M 0 18 0 52 9 26 0 346154 9 Suppose that Joe s Discount Store has received a shipment of 25 television sets 5 of which are defective On the following day 2 television sets are sold a Find the probability that both of the television sets are defective P both defective P 1st D 2nd D P 1st D P 2nd D 1st D 5 25 4 24 1 30 b Find the probability that at least one of the two television sets sold is defective D D 5 D D 5 D D 20 D D 25 4 24 1 30 25 20 24 5 30 25 5 24 5 30 P at least one D 1 30 5 30 5 30 11 30 OR P at least one D 1 P D D 1 20 25 19 24 1 19 30 11 30 10 Cards are drawn one by one without replacement from a standard 52 card deck What is the probability that a both the first and the second card drawn are s P 1st 2nd P 1st P 2nd 1st 13 52 12 51 1 17 b the first two cards drawn are a and a or a and a P 1st 2nd P 1st 2nd 13 52 13 51 13 52 13 51 c there are at least two s among the first three cards drawn 13 52 12 51 39 50 or 13 52 39 51 12 50 or 39 52 13 51 12 50 or 13 52 12 51 11 50 19968 132600 0 150588
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