homework_1_ans - Course MTH 1210 Feb 18’10...

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Unformatted text preview: Course MTH 1210 Feb 18’10 Homework #1 (answers ) PROBLEMS INVOLVING CONDITIONAL PROBABILITY [2] “Elementary Statistics” … [3] “Finite Math”… For solving a probability problem we should first of all properly identify and designate all types of events and corresponding probabilities given in the condition of the problem, and also the asked for probabilities. This includes the following steps. 1 . Designate the relevant primary events with convenient capital letters A, B , … (with or without _ subscripts); also designate the complementary events Ā, B, … (with or without subscripts) if necessary. Introduce the corresponding probabilities _ P(A) = P(B) = P(A i ) = P(B i ) = P(Ā) = P(B) 2. Designate properly the relevant compound events: A∩B , (A and B) , A U B (A or B) , A|B , B|A … Introduce the corresponding probabilities P(A∩B) = P(A and B) = P(A U B) = P(A or B) = P(A|B) = P(B|A) = P(A∩B i ) = P(A and B i ) = P(A U B i ) = P(A or B i ) = P(A|B i ) = P(B i |A) = 3 . Evaluating the probabilities of compound events first of all make a decision: are the events in question mutually exclusive or not? dependent or independent? Then, on the basis of logical reasoning, make a decision which laws of probabilities and in which sequence should be used for computing the asked for probabilities. ---------------------------------------------------------------------------------------------- #1. {#5-21 ; {[2], pg. 155} Suppose that for some activity the probabilities of certain events A and B are as follows: P(A) = 0.3, P(B) = 0.4 , and P(A∩B) = P(A and B) = 0.12 . (a) What is P(A| B) ? (b) What is P(B|A) ? (c) Are the events A and B independent? [ANS : (a) 0.3; (b) 0.4 ; (c) YES] Solution . P(A∩B) P(A and B) (a) P(A|B) = ------------- = ----------------- = 0.12/0.4 = 0.3 it is equal to P(A) (5.3) P(B) P(B) P(A∩B) P(A and B) (b) P(B|A) = ------------- = ----------------- = 0.12/0.3 = 0.4 it is equal to P(B) (5.3a) P(A) P(A) ( c ) YES , the events A and B are independent because the relations (5.5) take place: P(A|B) = P(A) = 0.3, P(B|A) = P(B) = 0.4 , P(A∩B) = P(A)*P(B) = 0.12 #2. {#23; [3], pg. 359} Let {#23; [3], pg....
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This note was uploaded on 11/24/2011 for the course MATH 3000 taught by Professor Kzaer during the Spring '05 term at St. Johns College MD.

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homework_1_ans - Course MTH 1210 Feb 18’10...

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