Answer "true" or "false" to the following statements. (5pts)

For the following story, tell me (1) if the reasoner is plausibly seen as employing a judgment heuristic (2) if a judgment heuristic is being used what judgment heuristic the reasoner is likely using. (4pts)

6.) After World War I, France constructed a vast system of highly fortified bunkers (called "ouvrages"), minefields, and  tank traps along the French/German border.  The fortifications came to be known as the Maginot Line.  Because the French Army couldn't imagine any army getting through the Maginot Line, the French Army believed that is was highly improbable that the Nazi Army could successfully invade France. 

(1) Yes a heuristic is likely being used.
(2) The French army seems to estimate the likelihood of a successful Nazi invasion based upon the difficulty they have in imagining such a successful invasion given their collective experiences.  Thus, the French army seems to employ the availability heuristic since they use their collective remembered experiences as their samples. They estimate the frequency of a successful Nazi invasion given their collective experiences through ease of imaginability. Since the French army finds it difficult to imagine such a successful Nazi invasion, they seem to infer that the probability of such a successful invasion is low.

Use Probability Theory to Solve the Following Problem. Make Sure to Show Your Work. (6 Pts)

                                               P(A₁) x P(B given A₁)
P(A₁ given B) = -------------------------------------------------------------
                                [P(A₁) x P(B given A₁)] + [P(A₂) x P(B given A₂)]
 
   

11.) What are the odds of winning two of two 23,000,000 ticket lotteries if you buy one ticket for one lottery and two tickets for the other?

Use the restricted conjunction rule, since the outcome of each lottery is independent of the outcome of the other lottery.  Use classical probability to estimate the odds of winning each lottery.

P(L₁ and L₂) = P(L₁) x P(L₂)

P(L₁) = f/n = 1/23,000,000
P(L₂) = f/n = 1/23,000,000

   1/23,000,000 X 2/23,000,000 = 2/23,000,000²
 
 

12.) Dr. Jones believes that there is a .95 probability that Mengola has the diamond.  However, he discovers that Mengola's men are looking for him.  He realizes that there is a .6 chance that Mengola's men would look for him if Mengola had the diamond, and there's a .99 chance they'd look for him if Mengola didn't have the diamond.  What should Jones believe about the whereabouts of the diamond now?

To update probability in light of new evidence use Bayes' theorem.

                                               P(A₁) x P(B given A₁)
P(A₁ given B) = -------------------------------------------------------------
                                [P(A₁) x P(B given A₁)] + [P(A₂) x P(B given A₂)]
 

A₁= Dr. Jones' original probability estimate for Mengola having the diamond = .95

 A₂ = Dr. Jones' original probability estimate for Mengola NOT having the diamond = .05

P(B given A₁) = .6

P(B given A₂) = .99

 
                                              .95 x .6
P(M given B) = ---------------------------------
                                 [.95 x .6] + [.05 x .99]
 
 
 
 

13.)  The average high temperature in San Francisco (in the sense of mean, median and mode) this year was 70 F.  Clearly, one never needs to wear a coat in San Francisco.
 
 DISPERSION  is relevant here as well as the average lows.   Temperature variation could still be relatively large.
   

14.)  Guns are now involved in over 60% of all violent crimes, whereas they were involved in only 47% a decade ago.  Clearly, the presence of guns is making the average person less safe.
 
The average person is made less safe if there is increased violent crime or if  the involvement of guns in crimes makes the crimes more dangerous.  This statistic does not address either of these questions.  

This section will appear on your tests only if your class completed the lectures on section 9.5

Use Your Knowledge of Scientific Method to Criticize the Following Argument (4pts):

15.)  Introspectionist psychologist would train subjects to introspect "correctly" for many,  many hours before gathering data by allowing  them to introspect while performing mental operations.
 
Extensive training by experimenter in how to introspect might introduce reporting bias in subject's reports.