ASSIGNMENT
Q.1) Suppose that in a senior college class of 500 students it is found that 210 smoke, 258 drink alcoholic beverages, 216 eat between meals, 122 smoke and drink alcoholic beverages, 83 eat between meals and drink alcoholic beverages, 97 smoke and eat between meals, and 52 engage in all three of these bad health practices. If a member of this senior class is selected at random, find the probability that the student
(a) Smokes but does not drink alcoholic beverages;
(b) Eats between meals and drinks alcoholic beverages but does not smoke;
(c) Neither smokes nor eats between meals.
Q.2) The probability that an American industry will locate in Shanghai, China is 0.7, the probability that it will locate in Beijing, China is 0.4, and the probability that it will locate in cither Shanghai or Beijing or both is 0.8. What is the probability that the industry will locate
(a) in both cities?
(b) in neither city?
Q.3) Given 2 events and for which P(R) = 0.46 and P(T) =0.32 and R(R∩T)= 0.19, find
- P(R')
- P(T')
- P(R U T)
- P(R'∩T)
- P(R' ∪T)
- P(R∩T')
Q.4) The probability that a woman trying on a dress will ask to have it altered is 0.65, the probability that she will ask to have it delivered to her home is 0.32, and the probability that she will ask to have both done is 0.21. What is the probability that a woman shopping in this store will ask
- either to have the dress altered or to have it delivered to her home
- neither to have it altered nor to have it delivered to her home
Q.5) If A and B are independent events and P(A) = 0.30 and P(B) = 0.60, find
- P(A)
- P(A∩B)
- P(A∪B)
- P(A'∩B')
Q.6) Given P(A) = 0.4, P(B) = 0.3, and P(B'/A') = 0.2, find
- P(A')
- P(B')
- P(B)
- P(A∩B)
- P(A/B)
Q.7) Select the best answer for the following
1. Which of the following cannot be a probability?
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(A) 5/3
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B) 2/3
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C) 3/5
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D) 1/2
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2. Which of the following cannot be a probability?
Q.8) The data about smoker is given as:
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Non-smoker
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Occasional smoker
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Regular smoker
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Heavy smoker
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Total
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Men
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370
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45
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61
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39
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515
|
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Women
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443
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39
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84
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38
|
604
|
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Total
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813
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84
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145
|
77
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1119
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a. If one of the 1119 people is randomly selected, find the probability of getting a regular or heavy smoker.
b. If two different people are randomly selected from the 1119 subjects, find the probability that they are both heavy smokers.
c. If two different people are randomly selected from the 1119 subjects, find the probability that they are both women
d. If one of the 1119 subjects is randomly selected, find the probability that the person chosen is a woman given that the person is an occasional smoker
e. If one of the 1119 subjects is randomly selected, find the probability that the person chosen is a non-smoker given that it is a woman.
Q.9) If R is the event that a convict committed armed robbery and D is the event that the convict pushed dope, state in words what probabilities are expressed by
(a) P(R\D);
(b) P(D'\R);
(c) P(R'\D').
Q.10) A random sample of 200 adults are classified below by sex and their level of education attained.
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Education
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Male
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Female
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Elementary
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38
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45
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Secondary
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28
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50
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College
|
22
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17
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If a person is picked at random from this group, find the probability that
(a) the person is a male, given that the person has a secondary education;
(b) the person does not have a college degree, given that the person is a female.
Q.11) In the senior year of a high school graduating class of 100 students, 42 studied mathematics, 68 studied psychology, 54 studied history, 22 studied both mathematics and history, 25 studied both mathematics and psychology, 7 studied history but neither mathematics nor psychology, 10 studied all three subjects, and 8 did not take any of the three. If a student is selected at random, find the probability that
(a) a person enrolled in psychology takes all three subjects;
(b) a person not taking psychology is taking both history and mathematics.
Q.12) The probability that a vehicle entering the Luray Caverns has Canadian license plates is 0.12; the probability that it is a camper is 0.28; and the probability that it is a camper with Canadian license plates is 0.09. What is the probability that
(a) a camper entering the Luray Caverns has Canadian license plates?
(b) a vehicle with Canadian license plates entering the Luray Caverns is a camper?
(c) a vehicle entering the Luray Caverns does not have Canadian plates or is not a camper?