In a certain engineering school of a university 60 of the st

In a certain engineering school of a university, 60% of the students are employed and 80% of the students are full?time.  Ninety percent of the employed are full?time students.

41. The probability that a student selected at random is  employed or a full?time student is:

(a) 0.92     

(b) 0.74

(c) 0.54

(d) 0.86

42. What percentage of students is neither full?time student nor employed?

(a) 0.09

(b) 0.14

(c) 0.24

(d) 0.86

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A company is launching a publicity campaign for a new product it has just introduced in the market.  The marketing manager decided to use three billboards on either side of I? 15 freeway to advertise the product.  These billboard locations were selected based on the probabilities the billboards would be noticed by the passing drivers. The agency that owns the billboards told the marketing manager that the probabilities the three billboards will be noticed by the drivers are 85%, 82%, and 90% respectively. Suppose that the probability that a billboard will be noticed by a passing driver is independent of whether the driver notices the other billboards.

43. The probability that someone driving on the freeway will notice all the three billboards is

(a) 0.6273     

(b) 0.7056

(c) 0.5032

(d) 0.3323

44. The probability that a driver will notice the first and third billboard but not the second:

(a) 0.075     

(b) 0.155

(c) 0.004

(d) 0.138

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A survey was conducted to know the investment preference and education level of Americans. The result of the survey showed that 72% of all investors who invested in Dow Jones stock index had some college degree. The survey also showed that 32% of all Americans have some college education and 26% of Americans own stocks.   Hint: Let  C= event that an investor has college degree,  S=  event that an investors owns stocks

45. The probability that a randomly selected investor has college degree and owns stocks :

(a) 0.1745     

(b) 0.0832

(c) 0.1872

(d) 0.1643                                          

46. The probability that a randomly selected investor has college degree or owns stocks :

(a) 0.30

(b) 0.39

(c) 0.28

(d) 0.58

47. The probability that a randomly selected investor neither has college degree nor owns stock :

(a) 0.50

(b) 0.69

(c) 0.78

(d) 0.61

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48. Suppose A, B, and C are three events with probabilities

P(A) = 0.45        P(B) = 0.30        P(C) = 0.15

The probability, P (A and B and C) or,   

P(A (union) B (union) C)

given that A, B and C are mutually exclusive is:

(a) 0.15

(b) 0.00

(c) 0.02

(d) 0.03

Solution

(41) Given

P(employed)=0.6

P(full time students)=0.8

P(full time students|employed)=0.9

--> P(employed and full time students)/P(employed) =0.9

--> P(employed and full time students) =0.9*0.6 = 0.54

So the probability is

P(employed or a full time student)

=P(employed) + P(full time student)- P(both)

=0.6+0.8 - 0.54

=0.86

Answer: (d) 0.86

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(42) The probability is

P(neither full time student nor employed)

= 1-P(employed or a full time student)

=1-0.86 =0.14

Answer: (b) 0.14

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(43) The probability is 0.85*0.82*0.9= 0.6273

Answer: (a) 0.6273

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(44) The probability is 0.85*(1-0.82)*0.9 = 0.1377

Answer: (d) 0.138

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(45) Given

P(S)=0.26

P(C)=0.32

P(C|S)=0.72

--> P(C and S)/P(S) =0.72

--> P(C and S) = 0.72*0.26 =0.1872

Answer: (c) 0.1872

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(46) The probability is

P(college degree or owns stocks)

=P(college degree)+ P(owns stocks) - P(both)

= 0.32+0.26 - 0.1872

=0.3928

Answer: (b) 0.39

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(47) P(neither has college degree nor owns stock)

=1-P(college degree or owns stocks)

=1-0.3928 =0.6072

Answer: (d) 0.61

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(48)P (A and B and C) =0

Answer: (b) 0.00