math 301 2996

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

This preview shows pages 1–3. Sign up to view the full content.

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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
1 to 5 on those from an urn, without replacement and pulling two out in the ﬁrst time.
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

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

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online