a. Explanation Given info: The table shows the well failures for different geological formation groups in Baltimore Country. Also, A denotes the event that the geological formation has more than 1000 wells, and let B denote the event that a well failed. Calculation: From the given information, A denotes the event that the geological formation has more than 1000 wells, and let B denote the event that a well failed. Therefore, the probability of a failure given there are more than 1,000 wells in a geological formation can be denoted as P ( B | A ) . The table for the given data is, Geological Formation Group Well Failed Total Gneiss 170 1,685 Granite 2 28 Loch raven schist 443 3,733 Mafic 14 363 Marble 29 309 Pretty boy schist 60 1,403 Other schists 46 933 Serpentine 3 39 Total 767 8,493 Multiplication Rule: If A and B are two events with P ( B ) ≠ 0 then, P ( A ∩ B ) = P ( A ) P ( B | A ) The formula for probability of event A is, P ( A ) = Frequency for the class Total frequencies in the distribution Substitute 6,821 for ‘Frequency for the class’ and 8,493 for ‘Total frequencies in the distribution’, P ( A ) = 6 , 821 8 , 493 = 0 b. To determine Find the probability of A ∪ B . c. To determine Find the probability of A ′ ∪ B ′ . d. To determine Find the probability of A using the total probability rule.

Applied Statistics and Probability for Engineers

6th Edition

ISBN: 9781118539712

Author: Douglas C. Montgomery

Publisher: WILEY

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Chapter 2.5, Problem 135E

To determine

Find the probability of A∩B.

To determine

Find the probability of A∪B.

To determine

Find the probability of A′∪B′.

To determine

Find the probability of A using the total probability rule.

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Chapter 2.5, Problem 134E

Chapter 2.5, Problem 136E

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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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Find the probability of A ∩ B .

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Find the probability of A∩B.

Find the probability of A∪B.

Find the probability of A′∪B′.

Find the probability of A using the total probability rule.

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Chapter 2 Solutions