11.5 Or and And Problems 711 conducted with 24 patients. After the study was concluded, it was determined that 16 patients reacted favorably to the medicine, 5 reacted unfavorably, and 3 were unaffected. If three of the patients are randomly selected, determine the probability of each of the following. 77. All the patients reacted favorably. 70 253 78. All the patients reacted unfavorably. 5 1012 79. None of the patients reacted favorably. 7 253 80. At least one of the patients reacted favorably. 246 253 Two Wheels In Exercises 81–84, suppose that you spin the double wheel shown below. Assuming that the wheels are independent and each sector is equally likely, determine the probability that you get 81. blue on both wheels. 1 24 82. red on the outer wheel and blue on the inner wheel. 1 12 83. a color other than red on both wheels. 5 12 84. red on at least one wheel. 7 12 85. Exam Preparation Professor Nguyen is in charge of a program to prepare students for a high school equivalency exam. Records show that the probability that a student in the program needs help in mathematics is 0.7, the probability that a student needs help in English is 0.6, and the probability that a student needs help in both mathematics and English is 0.55. Determine the probability that a student in the program needs help in mathematics or English. 0.75 86. Car Repair The manager at Arango Automotive has determined that the probability that a car brought into the shop requires an oil change is 0.6, the probability that a car brought into the shop requires brake repair is 0.2, and the probability that a car requires both an oil change and brake repair is 0.1. For a car brought into the shop, determine the probability that the car will require an oil change or brake repair. 0.7 Hitting a Target In Exercises 87–92, the probability that a heat-seeking torpedo will hit its target is 0.4. If the first torpedo hits its target, the probability that the second torpedo will hit the target increases to 0.9 because of the extra heat generated by the first explosion. 87. Are the events of firing two heat-seeking torpedoes at a target independent events? No 88. If one heat-seeking torpedo is fired at a target, determine the probability that it hits the target. 0.4 If two heat-seeking torpedoes are fired at a target, determine the probability that 89. neither hits the target. 0.36 90. the first hits the target and the second misses the target. 0.04 91. both hit the target. 0.36 92. the first misses the target and the second hits the target. 0.24 Polygenic Conditions In Exercises 93–98, certain congenital conditions are polygenic in nature. Typically, the chance that a child will be born with a polygenic condition is small. However, once a child is born with a polygenic condition, the probability that future children from the same parents will be born with the same condition increases. Assume that the probability of a child being born with polygenic condition A is 0.001. If a couple has a child with this condition, then the probability that the same couple has another child with the same condition becomes 0.04. 93. Are the events of children being born, from the same parents, having the polygenic condition independent events? No 94. A couple plans to have one child. Determine the probability that the child will be born with the condition. 0.001 If a couple plans to have two children, determine the probability that 95. both children will be born with the condition. 0.00004 96. the first will be born with the condition and the second will not. 0.00096 97. the first will not be born with the condition and the second will. 0.000999 98. neither will be born with the condition. 0.998001 Challenge Problems/Group Activities 99. Picking Chips A bag contains five red chips, three blue chips, and two yellow chips. Two chips are selected from the bag without replacement. If each chip is equally likely to be selected, determine the probability that two chips of the same color are selected. 14 45 100. Peso Coins Martin has ten coins from Mexico: three 1-peso coins, one 2-peso coin, two 5-peso coins, one
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