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Probability question that has to do with Course of action and calculation of expected numbers

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There are three scenarios under consideration that would trigger the NEO. We will call them A, B, and C.

Scenario A involves a coup attempt.

  • Scenario B involves hostilities commencing against a neighboring US ally.
    • Scenario C involves internal terrorism directed against US nationals.
    • We have tentatively assigned each of these “trigger” scenarios the following probabilities.
  • 
P(A) = .3

P(B) = .2

P(C) = .5

We believe that a network attack (N) against the JTF might be part of the scenarios. Based on preliminary analysis, the chance of a network attack depends on the scenario. We have the following probabilities:

P(N|A)=.3

P(N|B)=.9

P(N|C)=.1

We have two friendly courses of action (COA), I and II. The following table depicts expected friendly losses for each course of action and scenario.

We use failed log-in attempts on our non-classified PAO server as an (unclassified) intensity indicator of the likelihood of attacks on the secure systems. The time between failed log-in episodes (one episode might include several attempts by the same user until he/she is locked out) is well modeled by the exponential distribution with a mean of forty minutes.

  • (8 points) Devise a rule based on failed log-in episodes that would indicate that we are experiencing a network attack. The rule should have a false alarm rate of only 1%.
  • (8 points) Given that your rule has indicated a network attack, revise the probabilities for the different scenarios.
  • (8 points) Using those revised probabilities, calculate the expected number of casualties for COA I and II.
  • (8 points) Using the revised probabilities, draw the CDF for the number of casualties under COA I and II on the same graph.
  • (8 points) In your professional opinion, which COA do you recommend? Why? Justify your decision in writing.

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