TAILIEUCHUNG - Wiley the official guide for GMAT Episode 1 Part 4

Tham khảo tài liệu 'wiley the official guide for gmat episode 1 part 4', ngoại ngữ, ngữ pháp tiếng anh phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Math Review Arithmetic The probability that E does not occur is P not E 1 - P E . The probability that E or F occurs is P E or F P E P F - P E and F using the general addition rule at the end of section Sets . For the number cube if E is the event that the outcome is an odd number 1 3 5 and F is the event that the outcome is a prime number 2 3 5 then P E and F P 3 5 and . 3 3 2 4 6 so P E or F P E P F -P E and F y y-y y. 6 6 6 6 1 2 3 5 4 Note that the event E or F is E u F 1 2 3 5 and hence P E or F --------- 4. If the event E and F is impossible that is E n F has no outcomes then E and F are said to be mutually exclusive events and P E and F 0. Then the general addition rule is reduced to P E or F P E P F . This is the special addition rule for the probability of two mutually exclusive events. Two events A and B are said to be independent if the occurrence of either event does not alter the probability that the other event occurs. For one roll of the number cube let A 2 4 6 and let A 3 1 . . B 5 6 . Then the probability that A occurs is P A yL y T while presuming B occurs the probability that A occurs is 6 6 2 A n Bl INI 1 Bl 5 6 2. B 2 Similarly the probability that B occurs is P B 1 I probability that B occurs is 66 while presuming A occurs the lB n A l 6 l 1 a 2 4 6 3. Thus the occurrence of either event does not affect the probability that the other event occurs. Therefore A and B are independent. The following multiplication rule holds for any independent events E and F P E and F P E P F . For the independent events A and B above P A and 2 P AỴPỤĨ I Th Th Th . 2 3 6 Note that the event A and B is A n B 6 and hence P A and B P 6 y. It follows from 6 the general addition rule and the multiplication rule above that if E and F are independent then P E or F P E P F - P E P F . For a final example of some of these rules consider an experiment with events A B and C for which P A P B and P C . Also suppose that events A and B are mutually .

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