Test 1 Solution

Test 1 Solution - the middle digit. Therefore 5 4 4 9 8 7...

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STAT 230 Quiz #1 Sept 29, 2004 For all of the problems below, show your work in the space indicated! Name: I.D. No.: Section No. [_____/12] 1. Three digits are selected from 1,2, ,9 without replacement and randomly placed in a row. [4] (a) What is your sample space S for this random experiment? How many points are in S ? A possible choice of sample space S 123,213,321,. ..124,. ..789 i.e. all arrangements of 3 things taken from 9. There are 9 3 points in this S . (Note: -there may be more than one right answer) [4] (b) What is the probability that the first digit is 1 and last digit is 9? There is 1 way of choosing the number (1 for the first digit, for each of these, 1 way of choosing the number 9 for the last digit and 7 ways of choosing a number from the remaining for the middle digit. Therefore 1 7 1 9 8 7 1 72 [4] (c) What is the probability of the arrangement (odd number,even number,odd number)? There are five ways of selecting an odd number for the first digit and for each there are 4 ways of choosing an odd number for the third and 4 choices of even number for
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Unformatted text preview: the middle digit. Therefore 5 4 4 9 8 7 [_____/12] 2. Suppose A , B , C are all independent events with P A 0.3, P B 0.4, P C 0.5. [4] (a) Find P A B C The easiest way of doing this is to use part (c) and take 1 the answer to part (c). Otherwise use the fact that A , B , C are all independent and then P A B C P A P B P C P AB P BC P AC P ABC 0.7 0.4 0.5 0.7 0.4 0.4 0.5 0.7 0.5 0.7 0.4 0.5 [4] (b) Find P A B By independence of B , A this is P A B P A P B 0.3 0.6 0.18 [4] (c) Find the probability that none of the events A , B or C occur. This is P A B C P A P B P C 0.3 0.6 0.5 Alternative: use 1 answer to part (a)....
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Test 1 Solution - the middle digit. Therefore 5 4 4 9 8 7...

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