math 301 2996

math 301 2996 - Therefore, the answer is ( 5 2 ) * 3! = 60...

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HW3 Solution 1 Section 3.1 1.1 Problem 3 For each bit, two choices (either 0 or 1) are available. Therefore for a word consisting a string of 32 bits, 2 32 different possibilities are available. 1.2 Problem 6 This problem is the same as arranging n people in a line and then form a circle in the same order. Arranging n people in a line, we have n ! ways. Since relative positions rather than actual positions matters, each order is counted n times. Therefore the ways to arrange n people in a circle without taking into account the actual positions are n ! /n = ( n - 1)! . 1.3 Problem 14 Part a If every button being used once, the possible combinations are equal to the possible ways of pulling 5 balls with number 1 to 5 on those from an urn, without replacement. Therefore, the answer is 5! = 120 . Part b Now we can also press two buttons simultaneous and the other three one at a time (assump- tion from part a that each number being used once still holds). Under this circumstance, the possible combinations are equal to the possible ways of pulling 5 balls with number 1
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1 to 5 on those from an urn, without replacement and pulling two out in the first time.
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Unformatted text preview: Therefore, the answer is ( 5 2 ) * 3! = 60 . 2 Section 3.2 2.1 Problem 18 Let X stands for the number of correct answers. If by guessing, the probability of answering correctly for each question is 1 / 2. P ( X 2) = i =2 X i =0 10 i ( . 5) 10 = 0 . 05469 P ( X = 0) = 10 ( . 5) 10 = 0 . 00098 Now it is a binomial problem for comment Prosser or Crowell. Prosser: Binomial (340 , . 05469) Let Y denote the number of students getting 2 or fewer answers correct. P ( Y 1) = 1-P ( Y = 0) (1) = 1- 340 * (1-. 05469) 340 * (0 . 05469) (2) = 1-3 . 491534 * 10-9 (3) = 1 (4) within 5 digits after decimal place (5) Crowell: Binomial (340 , . 00098) Let Z denote the number of students getting 0 answers correct. P ( Z 1) = 1-P ( Z = 0) (6) = 1- 340 * (1-. 00098) 340 * (0 . 00098) (7) 2 = 1-. 71651 (8) = 0 . 28349 (9) Therefore, we know that Proseer is correct. 3...
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math 301 2996 - Therefore, the answer is ( 5 2 ) * 3! = 60...

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