A. Probability Problems 1. The president of a company has a hunch that there is
ID: 3125056 • Letter: A
Question
A. Probability Problems
1. The president of a company has a hunch that there is a 0.80 probability that the company will be successful in marketing a new brand of ice cream. Is this a case of classical, empirical or subjective probability? Explain your answer.
2. In a large city, 15,000 workers lost their jobs last year. Of them, 7400 lost their jobs because their companies closed down or moved, 4600 lost their jobs due to insufficient work, and the remainder lost their jobs because their positions were abolished. If one of these 15,000 workers is selected at random, find the probability that this worker lost his or her job
a) because the company closed down or moved?
b) due to insufficient work?
c) because the position was abolished?
3. A group of 2000 randomly selected adults were asked if they are in favor or against cloning. The following table gives the responses.
In Favor
Against
No Opinion
Total
Male
395
405
100
900
Female
300
680
120
1100
Total
695
1085
220
2000
Questions:
a) Are the events “male” and “in favor” mutually exclusive? Justify your answer.
b) Are the events “in favor” and ‘against” mutually exclusive? Justify your answer.
c) If one person is selected at random from these 2000 adults, find the probability that this
person is in favor of cloning.
d) What is the probability of randomly selecting a person who is against cloning.
e) What is the probability of randomly selecting a male person or a person who is against
cloning.
f) What is the probability of randomly selecting a female who is in favor of cloning.
g) What is the probability of randomly selecting a person who is against cloning or who has no
opinion at all.
In Favor
Against
No Opinion
Total
Male
395
405
100
900
Female
300
680
120
1100
Total
695
1085
220
2000
Explanation / Answer
1. It is Subjective Probabilty
2.
The probability that this worker lost his or her job because the company closed down or moved is 7400 / 15000 =0.4933
The probability that this worker lost his or her job due to insufficient work is 4600 / 15000 = 0.30667
The probability that this worker lost his or her job because the position was abolished is 3000 / 15000 = 0.2
3.
a) Events Male and in favor are not mutually exclusive since P(Male and in Favor) =395/2000 = 0.1975
b) The events “in favor” and ‘against” are mutually exclusive since P(in favor and against) = 0
c) the probability that this person is in favor of cloning is P(In Favor) = 695/2000 = 139/400 = 0.3475
d) The probability of randomly selecting a person who is against cloning = 1085/2000 = 0.5425
e) The probability of randomly selecting a male person or a person who is against cloning.
P(Male or against) = P(Male) + P(againstr) - P(Male and against)
=(900/2000) +(1085/2000) - (405/2000) = 1580/2000=0.79
f) The probability of randomly selecting a female who is in favor of cloning is
P(Feamale and infavor) = 300/ 2000 =0.15
g)
the prrbability of randomly selecting a person who is against cloning or who has no opinion at all
P(against or no opinion) = P(againts) + P(no opinion) = (1085/2000) + (220/2000) = 0.6525