230hw1 - MATH 230 HOMEWORK 1(Due Tuesday[Please submit your...

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October 12, 2009 MATH 230 HOMEWORK # 1 (Due: October 20, 2009, Tuesday) [Please, submit your homework to my office (SA 105) by 5:30 PM] (DO NOT forget to write your Section number) 1. There are 2 boxes, each has r balls numbered from 1 through r . A random sample of n balls is drawn ( r n ) without replacement from each box. Find the probability that the samples contain exactly k having the same numbers in common. 2. Let A 1, A 2 and B 1 , B 2 events such that 5 . 0 ) ( ) ( 1 1 = = B P A P and 6 . 0 ) ( 1 2 = A A P , 4 . 0 ) ( 1 2 = A B P , 4 . 0 ) ( 1 2 = B A P , 6 . 0 ) ( 1 2 = B B P . Show that 5 . 0 ) ( ) ( 2 2 = = B P A P 3. Consider the experiment of rolling two dice. Define the events A, B, C so that A= {First die results in a 1, 2, or 3} B= {second die results in a 4, 5, or 6} C= {The sum of two faces is 7} Show that A, B and C are pairwise independent but not (mutually) independent. 4. In a customer satisfaction survey, 5 3 of those surveyed had a Japanese-made car, 10 3 European-made car, and
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230hw1 - MATH 230 HOMEWORK 1(Due Tuesday[Please submit your...

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