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Sets, Combinatorics, and Probability
72. On a particular manufacturing job, the probability that there will be a shortage of copper is 0.37. The probability that there will be a shortage of both copper and aluminum is 0.28. Find the probability of a shortage
of aluminum given a shortage of copper.
73. In Example 71,
a. What is the probability that a patient responds positively to compound A given that he or she responds
positively to B?
b. What is the probability that a patient responds positively to either compound A or compound B?
c. What is the probability that a patient does not respond positively to either compound?
74. A food magazine surveys the preferences of its readers who like Asian food. The findings follow.
47% like Thai food
(E 1 )
39% like Indian food
(E 2 )
78% like Chinese food
(E 3 )
23% like both Thai and Indian food
31% like both Indian and Chinese food
29% like both Thai and Chinese food
a. Extend observation 5 in Table 4.3 to the case of three events, E 1 , E 2 , and E 3 .
b. Find the probability that a reader likes all three types of food.
c. Find the probability that a reader likes Chinese food given that the reader likes Indian food.
For Exercises 75−80, a student takes a true−false quiz with four questions, each equally likely to be either T or F.
75. What is the probability of getting exactly one question wrong?
76. What is the probability of getting Question 1 correct?
77. What is the probability of getting three or more questions correct?
78. What is the probability of getting the first two questions correct?
79. What is the probability of getting the first two questions correct given that the answer to Question 1 is
correct?
80. What is the probability of getting all four questions correct given that the answers to the first two questions
are correct?
For Exercises 81−88, a family has 3 children; boys and girls are equally likely offspring.
81. What is the probability that the oldest child is a boy?
82. What is the probability that the youngest two children are girls?
83. What is the probability of 2 boys and 1 girl?
84. What is the probability of no girls?
85. What is the probability of at least 1 girl?
86. What is the probability of 3 girls?
87. What is the probability of 3 girls given that the first 2 are girls?
88. What is the probability of at least 1 boy and at least 1 girl given that there is at least 1 boy?
Sets, Combinatorics, and Probability
72. On a particular manufacturing job, the probability that there will be a shortage of copper is 0.37. The probability that there will be a shortage of both copper and aluminum is 0.28. Find the probability of a shortage
of aluminum given a shortage of copper.
73. In Example 71,
a. What is the probability that a patient responds positively to compound A given that he or she responds
positively to B?
b. What is the probability that a patient responds positively to either compound A or compound B?
c. What is the probability that a patient does not respond positively to either compound?
74. A food magazine surveys the preferences of its readers who like Asian food. The findings follow.
47% like Thai food
(E 1 )
39% like Indian food
(E 2 )
78% like Chinese food
(E 3 )
23% like both Thai and Indian food
31% like both Indian and Chinese food
29% like both Thai and Chinese food
a. Extend observation 5 in Table 4.3 to the case of three events, E 1 , E 2 , and E 3 .
b. Find the probability that a reader likes all three types of food.
c. Find the probability that a reader likes Chinese food given that the reader likes Indian food.
For Exercises 75−80, a student takes a true−false quiz with four questions, each equally likely to be either T or F.
75. What is the probability of getting exactly one question wrong?
76. What is the probability of getting Question 1 correct?
77. What is the probability of getting three or more questions correct?
78. What is the probability of getting the first two questions correct?
79. What is the probability of getting the first two questions correct given that the answer to Question 1 is
correct?
80. What is the probability of getting all four questions correct given that the answers to the first two questions
are correct?
For Exercises 81−88, a family has 3 children; boys and girls are equally likely offspring.
81. What is the probability that the oldest child is a boy?
82. What is the probability that the youngest two children are girls?
83. What is the probability of 2 boys and 1 girl?
84. What is the probability of no girls?
85. What is the probability of at least 1 girl?
86. What is the probability of 3 girls?
87. What is the probability of 3 girls given that the first 2 are girls?
88. What is the probability of at least 1 boy and at least 1 girl given that there is at least 1 boy?