Homework_1 - St Johns University Department of Mathematics...

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St. John’s University Department of Mathematics and Computer Science Course MTH 1210 Homework #1 (NON-CHECKABLE) Feb 10’07 PROBLEMS INVOLVING CONDITIONAL PROBABILITY #1. 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] #2. Let A and B be independent events with probabilities P(A) = ¼ and P(B) = 1/5 . Find the probabilities P(A∩B) and P(A U B) . [ANS: 1/20; 2/5] #3. Determine whether or not each of the following pairs of events is independent. (a) rolling a pair of dice and observing a “2” on the first die and a “2” on the second die; (b) drawing a “heart” from a regular deck of a playing cards and then drawing another “heart” from the same deck without replacing the first card; (c) same as (b) except the first card is returned to the deck before the second drawing;
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