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Q: A computer consulting firm presently has bids out on three projects. Let Ai = {awarded...

Q: A computer consulting firm presently has bids out on three projects. Let Ai = {awarded project i}, for i = 1, 2, 3, and suppose that P(A1) = 0.23, P(A2) = 0.25, P(A3) = 0.29, P(A1 ∩ A2) = 0.07, P(A1 ∩ A3) = 0.05, P(A2 ∩ A3) = 0.08, P(A1 ∩ A2 ∩ A3) = 0.02. Use the probabilities given above to compute the following probabilities, and explain in words the meaning of each one. (Round your answers to four decimal places.)

(a)    P(A2 | A1) =

Explain this probability in words.

If the firm is awarded project 2, this is the chance they will also be awarded project 1. If the firm is awarded project 1, this is the chance they will also be awarded project 2.     This is the probability that the firm is awarded either project 1 or project 2. This is the probability that the firm is awarded both project 1 and project 2.


(b)    P(A2 ∩ A3 | A1) =

Explain this probability in words.

This is the probability that the firm is awarded projects 1, 2, and 3. If the firm is awarded project 1, this is the chance they will also be awarded projects 2 and 3.     If the firm is awarded projects 2 and 3, this is the chance they will also be awarded project 1. This is the probability that the firm is awarded at least one of the projects.


(c)    P(A2 ∪ A3 | A1) =

Explain this probability in words.

If the firm is awarded project 1, this is the chance they will also be awarded at least one of the other two projects. This is the probability that the firm is awarded at least one of the projects.     If the firm is awarded at least one of projects 2 and 3, this is the chance they will also be awarded project 1. This is the probability that the firm is awarded projects 1, 2, and 3.


(d)    P(A1 ∩ A2 ∩ A3 | A1 ∪ A2 ∪ A3) =

Explain this probability in words.

This is the probability that the firm is awarded at least one of the projects. This is the probability that the firm is awarded projects 1, 2, and 3.     If the firm is awarded at least two of the projects, this is the chance that they will be awarded all three projects. If the firm is awarded at least one of the projects, this is the chance that they will be awarded all three projects.

Q: Three couples and two single individuals have been invited to an investment seminar and have agreed to attend. Suppose the probability that any particular couple or individual arrives late is 0.38 (a couple will travel together in the same vehicle, so either both people will be on time or else both will arrive late). Assume that different couples and individuals are on time or late independently of one another. Let X = the number of people who arrive late for the seminar.

(a) Determine the probability mass function of X. [Hint: label the three couples #1, #2, and #3 and the two individuals #4 and #5.] (Round your answers to four decimal places.)

x P(X = x)
  0        
  1        
  2        
  3        
  4        
  5        
  6        
  7        
  8        


(b) Obtain the cumulative distribution function of X. (Round your answers to four decimal places.)

x F(x)
  0        
  1        
  2        
  3        
  4        
  5        
  6        
  7        
  8        


Use the cumulative distribution function of X to calculate

P(2 ≤ X ≤ 7).

(Round your answer to four decimal places.)

P(2 ≤ X ≤ 7) =

Solutions

Expert Solution

milcah answered 1 year ago
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