a. To determine Find P ( A | B ′ ) . Explanation Given info: A computer system uses passwords that contain exactly eight characters, and each character is one of the 26 lowercase letters (a to z) or 26 uppercase letters (A to Z) or 10 integers (0-9). Let W denote the set of all possible password, and let A and B denote the events that consist of passwords with only letters or only integers, respectively. All passwords in Ω are equally likely. Calculation: From given information, W denote the set of all possible password, and let A and B denote the events that consist of passwords with only letters or only integers, respectively. Let B ′ denotes the events that consist of passwords with not only integers. Conditional Probability : The probability of an event B under the knowledge that the outcome will be in event A is called conditional probability and it is denoted by P ( B | A ) . It can be calculated as follows. P ( B | A ) = P ( A ∩ B ) P ( A ) From the given information, number of outcomes for A is 52 8 ( = ( 26 + 26 ) 8 ) , number of outcomes for B is 10 8 . The total number of outcomes in the sample space is 62 8 ( = 52 + 10 ) 8 . The formula for finding P ( A | B ′ ) is, P ( A | B ′ ) = P ( A ∩ B ′ ) P ( B ′ ) The formula for probability of A ∩ B ′ is, P ( A ∩ B ′ ) = Number of outcomes in A and B ′ Total number of outcomes in the sample space Substitute 52 8 for ‘Number of outcomes in A and B ′ ’ and 62 8 for ‘Total number of outcomes in the sample space’ P ( A ∩ B ′ ) = 52 8 62 8 Therefore, the probability of A ∩ B ′ is 52 8 62 8 b. To determine Find the probability P ( A ′ ∩ B ) . c. To determine Find P ( Password contains exactly 2 integers given that it contains at least 1 integer ) .

Applied Statistics and Probability for Engineers

6th Edition

ISBN: 9781118802250

Author: Montgomery

Publisher: WILEY

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Chapter 2.5, Problem 141E

To determine

Find P(A|B′).

To determine

Find the probability P(A′∩B).

To determine

Find P(Password contains exactly 2 integers given that it contains at least 1 integer).

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Chapter 2.5, Problem 140E

Chapter 2.6, Problem 142E

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Chapter 2 Solutions

Applied Statistics and Probability for Engineers

Ch. 2.1 - Provide a reasonable description of the sample...Ch. 2.1 - Provide a reasonable description of the sample...Ch. 2.1 - Provide a reasonable description of the sample...Ch. 2.1 - Provide a reasonable description of the sample...Ch. 2.1 - Provide a reasonable description of the sample...Ch. 2.1 - Provide a reasonable description of the sample...Ch. 2.1 - Provide a reasonable description of the sample...Ch. 2.1 - 2-18. Three attempts are made to read data in a...Ch. 2.1 - 2-19. Three events are shown on the Venn diagram...Ch. 2.1 - 2-20. Three events are shown on the Venn diagram...Ch. 2.1 - 2-21. A digital scale that provides weights to the...Ch. 2.1 - Prob. 22E Ch. 2.1 - 2-23. Go Tutorial Four bits are transmitted over...Ch. 2.1 - 2-24. In light-dependent photosynthesis, light...Ch. 2.1 - 2-25. In control replication, cells are replicated...Ch. 2.1 - 2-26. Disks of polycarbonate plastic from a...Ch. 2.1 - 2-27. Samples of a cast aluminum part are...Ch. 2.1 - 2-28. Samples of emissions from three suppliers...Ch. 2.1 - 2-29. The rise time of a reactor is measured in...Ch. 2.1 - Prob. 30E Ch. 2.1 - Prob. 31E Ch. 2.1 - 2-32. Counts of the Web pages provided by each of...Ch. 2.1 - 2-33. A reactor’s rise time is measured in minutes...Ch. 2.1 - 2-34. A wireless garage door opener has a code...Ch. 2.1 - Prob. 35E Ch. 2.1 - 2-36. In a manufacturing operation, a part is...Ch. 2.1 - 2-37. New designs for a wastewater treatment tank...Ch. 2.1 - 2-38. A manufacturing process consists of 10...Ch. 2.1 - Prob. 39E Ch. 2.1 - 2-40. In a sheet metal operation, three notches...Ch. 2.1 - Prob. 41E Ch. 2.1 - 2-42. In the layout of a printed circuit board for...Ch. 2.1 - 2-43. In the laboratory analysis of samples from a...Ch. 2.1 - 2-44. In the design of an electromechanical...Ch. 2.1 - 2-45. Consider the design of a communication...Ch. 2.1 - 2-46. A byte is a sequence of eight bits and each...Ch. 2.1 - 2-47. In a chemical plant, 24 holding tanks are...Ch. 2.1 - 2-48. Plastic parts produced by an...Ch. 2.1 - 2-49. A bin of 50 parts contains 5 that are...Ch. 2.1 - 2-50. The following table summarizes 204...Ch. 2.1 - 2-51. A Web ad can be designed from four different...Ch. 2.1 - 2-52. Consider the hospital emergency department...Ch. 2.1 - 2-53. An article in The Journal of Data Science...Ch. 2.1 - 2-54. Similar to the hospital schedule in Example...Ch. 2.1 - 2-55. Consider the bar code in Example 2-12. One...Ch. 2.1 - 2-56. A computer system uses passwords that...Ch. 2.1 - Prob. 57E Ch. 2.2 - 2-58. Each of the possible five outcomes of a...Ch. 2.2 - 2-59. The sample space of a random experiment is...Ch. 2.2 - 2-60. Orders for a computer are summarized by the...Ch. 2.2 - Prob. 61E Ch. 2.2 - Prob. 62E Ch. 2.2 - 2-63. An injection-molded part is equally likely...Ch. 2.2 - 2-64. In an acid-base titration, a base or acid is...Ch. 2.2 - Prob. 65E Ch. 2.2 - Prob. 66E Ch. 2.2 - 2-67. Suppose your vehicle is licensed in a state...Ch. 2.2 - Prob. 68E Ch. 2.2 - 2-69. Magnesium alkyls are used as homogenous...Ch. 2.2 - 2-70. Disks of polycarbonate plastic from a...Ch. 2.2 - 2-71. Samples of emissions from three suppliers...Ch. 2.2 - Prob. 72E Ch. 2.2 - Prob. 73E Ch. 2.2 - Prob. 74E Ch. 2.2 - 2-75. A Web ad can be designed from four different...Ch. 2.2 - Prob. 76E Ch. 2.2 - Prob. 77E Ch. 2.2 - 2-78. Consider the bar code in Example 2-12....Ch. 2.2 - 2-79. Similar to the hospital schedule in Example...Ch. 2.2 - Prob. 80E Ch. 2.2 - 2-81. A computer system uses passwords that...Ch. 2.3 - 2-82. If P(A) = 0.3, P(B) = 0.2, and P(A B) =...Ch. 2.3 - 2-83. If A, B, and C are mutually exclusive events...Ch. 2.3 - 2-84. In the article “ACL Reconstruction Using...Ch. 2.3 - 2-85. Disks of polycarbonate plastic from a...Ch. 2.3 - 2-86. Strands of copper wire from a manufacturer...Ch. 2.3 - 2-87. The analysis of shafts for a compressor is...Ch. 2.3 - 2-88. Cooking oil is produced in two main...Ch. 2.3 - 2-89. A manufacturer of front lights for...Ch. 2.3 - 2-90. A computer system uses passwords that are...Ch. 2.3 - 2-91. Consider the endothermic reactions in...Ch. 2.3 - 2-92. A Web ad can be designed from four different...Ch. 2.3 - Prob. 93E Ch. 2.3 - Prob. 94E Ch. 2.3 - 2-95. Consider the barcode in Example 2-12....Ch. 2.3 - Prob. 96E Ch. 2.3 - Prob. 97E Ch. 2.3 - Prob. 98E Ch. 2.4 - 2-99. Disks of polycarbonate plastic from a...Ch. 2.4 - 2-100. Samples of skin experiencing desquamation...Ch. 2.4 - 2-101. The analysis of results from a leaf...Ch. 2.4 - 2-102. Samples of a cast aluminum part are...Ch. 2.4 - 2-103. The following table summarizes the analysis...Ch. 2.4 - 2-104. Consider the data on wafer contamination...Ch. 2.4 - 2-105. The following table summarizes the number...Ch. 2.4 - 2-106. A maintenance firm has gathered the...Ch. 2.4 - 2-107. A lot of 100 semiconductor chips contains...Ch. 2.4 - 2-108. A batch of 500 containers for frozen orange...Ch. 2.4 - 2-109. A batch of 350 samples of rejuvenated...Ch. 2.4 - 2-110. A computer system uses passwords that are...Ch. 2.4 - 2-111. If , must A = B? Draw a Venn diagram to...Ch. 2.4 - 2-112. Suppose A and B are mutually exclusive...Ch. 2.4 - 2-113. Consider the endothermic reactions in...Ch. 2.4 - Prob. 114E Ch. 2.4 - Prob. 115E Ch. 2.4 - 2-116. An article in the The Canadian Entomologist...Ch. 2.4 - 2-117. Consider the bar code in Example 2-12....Ch. 2.4 - Prob. 118E Ch. 2.4 - Prob. 119E Ch. 2.4 - 2-120. A computer system uses passwords that...Ch. 2.5 - 2-121. Suppose that and . Determine the...Ch. 2.5 - Prob. 122E Ch. 2.5 - 2-123. The probability is 1% that an electrical...Ch. 2.5 - 2-124. Suppose 2% of cotton fabric rolls and 3% of...Ch. 2.5 - 2-125. The edge roughness of slit paper products...Ch. 2.5 - 2-126. In the 2012 presidential election, exit...Ch. 2.5 - 2-127. Computer keyboard failures are due to...Ch. 2.5 - 2-128. Heart failures are due to either natural...Ch. 2.5 - Prob. 129E Ch. 2.5 - Prob. 130E Ch. 2.5 - Prob. 131E Ch. 2.5 - 2-132. Consider the endothermic reactions in...Ch. 2.5 - Prob. 133E Ch. 2.5 - 2-134. Consider the hospital emergency room data...Ch. 2.5 - Prob. 135E Ch. 2.5 - Prob. 136E Ch. 2.5 - 2-137. A Web ad can be designed from four...Ch. 2.5 - 2-138. Consider the code in Example 2-12. Suppose...Ch. 2.5 - 2-139. Similar to the hospital schedule in Example...Ch. 2.5 - Prob. 140E Ch. 2.5 - 2-141. A computer system uses passwords that...Ch. 2.6 - 2-142. If , and , are the events A and B...Ch. 2.6 - 2-143. If , and , are the events B and the...Ch. 2.6 - 2-144. If , and A and B are mutually exclusive,...Ch. 2.6 - 2-145. A batch of 500 containers of frozen orange...Ch. 2.6 - 2-146. Disks of polycarbonate plastic from a...Ch. 2.6 - 2-147. Samples of emissions from three suppliers...Ch. 2.6 - 2-148. Redundant array of inexpensive disks (RAID)...Ch. 2.6 - 2-149. The probability that a lab specimen...Ch. 2.6 - 2-150. In a test of a printed circuit board using...Ch. 2.6 - 2-151. Six tissues are extracted from an ivy plant...Ch. 2.6 - 2-152. A player of a video game is confronted with...Ch. 2.6 - 2-153. In an acid-base titration, a base or acid...Ch. 2.6 - Prob. 154E Ch. 2.6 - Prob. 155E Ch. 2.6 - 2-156. The following circuit operates if and only...Ch. 2.6 - Prob. 157E Ch. 2.6 - Prob. 158E Ch. 2.6 - Prob. 159E Ch. 2.6 - Prob. 160E Ch. 2.6 - 2-161. A Web ad can be designed from four...Ch. 2.6 - Prob. 162E Ch. 2.6 - Prob. 163E Ch. 2.6 - 2-164. Table 2-1 provides data on wafers...Ch. 2.6 - 2-165. Table 2-1 provides data on wafers...Ch. 2.7 - Prob. 166E Ch. 2.7 - Prob. 167E Ch. 2.7 - Prob. 168E Ch. 2.7 - Prob. 169E Ch. 2.7 - 2-170. In the 2012 presidential election, exit...Ch. 2.7 - Prob. 171E Ch. 2.7 - 2-172. An inspector working for a manufacturing...Ch. 2.7 - 2-173. A new analytical method to detect...Ch. 2.7 - 2-174. Consider the endothermic reactions in...Ch. 2.7 - Prob. 175E Ch. 2.7 - Prob. 176E Ch. 2.7 - 2-177. Two Web colors are used for a site...Ch. 2.7 - Prob. 178E Ch. 2.7 - 2-179. An e-mail filter is planned to separate...Ch. 2.7 - 2-180. A recreational equipment supplier finds...Ch. 2.7 - Prob. 181E Ch. 2.8 - 2-182. Decide whether a discrete or continuous...Ch. 2.8 - 2-183. Decide whether a discrete or continuous...Ch. 2.8 - 2-184. Decide whether a discrete or continuous...Ch. 2 - Prob. 185SE Ch. 2 - 2-186. A sample of three calculators is selected...Ch. 2 - 2-187. Samples of a cast aluminum part are...Ch. 2 - 2-188. Shafts are classified in terms of the...Ch. 2 - 2-189. If A, B, and C are mutually exclusive...Ch. 2 - 2-190. The analysis of shafts for a compressor is...Ch. 2 - 2-191. A researcher receives 100 containers of...Ch. 2 - 2-192. A lot contains 15 castings from a local...Ch. 2 - 2-193. In the manufacturing of a chemical...Ch. 2 - 2-194. Incoming calls to a customer service...Ch. 2 - 2-195. A congested computer network has a 0.002...Ch. 2 - 2-196. Samples of a cast aluminum part are...Ch. 2 - 2-197. Go Tutorial An optical storage device uses...Ch. 2 - 2-198. Semiconductor lasers used in optical...Ch. 2 - 2-199. Energy released from cells breaks the...Ch. 2 - 2-200. A sample preparation for a chemical...Ch. 2 - 2-201. In circuit testing of printed circuit...Ch. 2 - 2-202. The data from 200 machined parts are...Ch. 2 - 2-203. Computers in a shipment of 100 units...Ch. 2 - 2-204. The probability that a customer’s order is...Ch. 2 - 2-205. Let E1, E2 and E3 denote the samples that...Ch. 2 - 2-206. Transactions to a computer database are...Ch. 2 - Prob. 207SE Ch. 2 - Prob. 208SE Ch. 2 - Prob. 209SE Ch. 2 - 2-210. The British government has stepped up its...Ch. 2 - Prob. 211SE Ch. 2 - 2-212. An encryption-decryption system consists of...Ch. 2 - 2-213. It is known that two defective copies of a...Ch. 2 - 2-214. A robotic insertion tool contains 10...Ch. 2 - Prob. 215SE Ch. 2 - Prob. 216SE Ch. 2 - 2-217. A lot of 50 spacing washers contains 30...Ch. 2 - Prob. 218SE Ch. 2 - Prob. 219SE Ch. 2 - Prob. 220SE Ch. 2 - 2-221. The following circuit operates if and only...Ch. 2 - 2-222. A company that tracks the use of its Web...Ch. 2 - Prob. 223SE Ch. 2 - Prob. 224SE Ch. 2 - Prob. 225SE Ch. 2 - 2-226. Natural red hair consists of two genes....Ch. 2 - Prob. 227SE Ch. 2 - Prob. 228SE Ch. 2 - Prob. 229SE Ch. 2 - Prob. 230SE Ch. 2 - Prob. 231SE Ch. 2 - 2-232. A biotechnology manufacturing firm can...Ch. 2 - 2-233. Assume the following characteristics of the...Ch. 2 - Prob. 234SE Ch. 2 - Prob. 235SE

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