A. Probability Problems 1. The president of a company has a hunch that there is

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   TotalMale  395   405    100   900Female 300   680    120  1100Total 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.  

Explanation / Answer

1) Empirical

as the prob is in number and based on past data

2) the probability that this worker lost his or her job

a) because the company closed down or moved = 7400/15000 = 0.4933

b) due to insufficient work=4600/15000 = 0.3067

c) because the position was abolished = 1-(0.4933+0.3067) = 0.2

a) No they are not mutually exclusive as common elements are 395

b) yes in favour and against are mutually exclusive

c) Prob for one person in favour of cloning = 695/2000 = 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

= Prob of a male + Prob of person again cloning - prob of male against cloning

= (900+1085-405)/2000 = 0.790

f) the probability of randomly selecting a person who is against cloning or who has no      opinion at all.

= (1085+220)/2000 = 0.6525

In favour Against No opinion Male 395 405 100 900 Female 300 680 120 1100 695 1085 220 2000

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