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Geometry: Statistics 12.4 Two events are disjoint or mutually exclusive if they have no outcomes in common. (i.e. ____________________ they do not overlap Example: A 6-sided die is rolled. Consider if the two events are disjoint or not disjoint. a) The result is an even number The result is a prime number not disjoint 2 is in both b) The result is a 2 or a 4 The result is an odd number disjoint The union of two events A and B is the set of outcomes that are in A or B or both The intersection of two events A and B is ________________________________ the outcomes that are in both A and B (i.e. the intersection is _____________________________ where the events A and B overlap disjoint P( A) P( B) P( A and B) P( A) P( B) Example: A card is randomly chosen from a standard deck of 52 cards. a) P(Ace or a face card) 12 4 disjo int b) P(spade or a face card) 12 13 3 of the face cards are spades 16 .308 52 13 12 3 22 .423 52 52 Example: Of the 200 students in a senior class, 113 are either varsity athletes or on the honor roll. 74 seniors are varsity athletes and 51 seniors are on the honor roll. What is the probability that a randomly selected senior is both a varsity athlete and on the honor roll? P(A or B) P(A) P(B) - P(A and B) 113 200 74 51 200 200 - 12 -P(A and B) 200 12 3 P(A and B) .06 200 50 Example: The American Diabetes Association estimates that 8.3% of people in the U.S. have diabetes. Suppose that a medical lab has developed a simple diagnostic test for diabetes that is 98% accurate for people who have diabetes and 95% accurate for people who do not have diabetes (i.e. the test gives a falsepositive). .98 .083 D .02 .05 .917 NoD .95 .08134 .00166 .04585 .87115 If the laboratory gives the test to a randomly selected person, what is the probability the test is correct? .08134 .87115 .95249 If the laboratory gives the test to a randomly selected person, what is the probability the person has diabetes given the test result is positive? P( D and ) P(diabetes | ) P() .08134 .640 .08134 .04585