20082ee131A_1_HW1SOL

20082ee131A_1_HW1SOL - 20 / 36 = 16 / 36 . h. Upon...

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EE 131A Homework #1 Solution Spring 2008 K. Yao 1. a. S = { S 2 ,...,S 10 ,SJ,SQ,SK,SA,H 2 ,...,HA,D 2 ,...,DA,C 2 ,...CA } . b. P ( Aceof Spade ) = 1 / 52 . c. P ( Ace ) = 4 / 52 = 1 / 13 . d. P ( card 10) = 20 / 52 = 5 / 13 . e. For the “biased deck of cards,” we have: (b.) P ( Aceof Spade ) = 1 / 32 . (c.) P ( Ace ) = 4 / 32 = 1 / 8 . (d.) P ( card 10) = 4 / 72 + 16 / 32 = 1 / 18 + 1 / 2 = 10 / 18 = 5 / 9 . 2. a. There are 6 favorable outcomes, (3 , 4) , (4 , 3) , (6 , 1) , (1 , 6) , (5 , 2) , (2 , 5) , so prob is 6 / 36. b. There are 8 favorable outcomes, (6 , 1) , (5 , 2) , (4 , 3) , (1 , 6) , (3 , 4) , (2 , 5) , (6 , 5) , (5 , 6) so prob 8 / 36 . c. There are 6 outcomes where the two dice are equal. Of the remaining 30 outcomes, half have second > first. Answer is 15 / 36. d. Favorable outcomes are (6 , 1) ,..., (6 , 6) , (1 , 6) ,..., (6 , 6) , but don’t count (6 , 6) twice. An- swer is 11 / 36. e. Favorable outcomes are (5 , 5) , (5 , 6) , (6 , 5) , (6 , 6). Answer is 4 / 36. f. Upon inspection in the sample space, there are twenty such outcomes out of 36. Answer is 20 / 36 . g. Upon inspection in the sample space, there are sixteen such outcomes out of 36. P ( neither over 4) = 1 - P ( atleastone 5) = 1 -
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Unformatted text preview: 20 / 36 = 16 / 36 . h. Upon inspection in the sample space, there are nine such outcomes out of 36. Answer is 9 / 36 . 3. The number of distinct ordered triplets with replacement = 7 2 52 = 728. 4. On the rst day, there is a choice of 5 pairs, and subsequently, there is a choice of only 4 pairs. Total number is = 5 4 4 4 4 4 = 5 4 5 = 5120. 5. There are 4! = 24 ways in which the four volumes can be put back. Only one of these is correct. P (correct order) = 1 4! = 1 24 . 6. The total number of ways of arranging the word cold is 4! = 24. In considering the total number of ways of arranging the word cool, the letter o is repeated twice, thus 2! arrangements are the same. Thus, total number of ways of arranging the word cool is 4! / 2! = 24 / 2 = 12....
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This note was uploaded on 04/12/2010 for the course EE 131A taught by Professor Lorenzelli during the Spring '08 term at UCLA.

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