Methods for Solving Problems Coursera Quiz Answers

Get All Weeks Methods for Solving Problems Coursera Quiz Answers

Methods for Solving Problems Week 01 Quiz Answers

Quiz 1: Recognizing and Solving Problems

Q1. In the chapter by Pretz et al., there is a discussion of “well-defined” versus “ill-defined” problems. Which of the following is true of ill-defined problems?

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Ill-defined problems generally don’t lend themselves to “problem-space” representation.

Q2. The Chase-Simon “chess memory” experiment illustrates which of the following ideas?

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Chess experts internally represent chess games differently than do novices, and thus have better memory for realistic chess board positions than do novices.

Q3. Suppose we have a problem space representation in which the (lone) goal state can be reached via a sequence of edges from some states but not others. Which of the following statements is true of this problem (and its graph)?

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As long as our start state is among the states with paths to the goal state, then we can consider this problem solvable.

Q4. Which of the following best describes (on the basis of experimental evidence) people’s use of logical reasoning?

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People are capable of reasoning logically, but it takes effort and they do so inconsistently (depending on context) in everyday situations.

Methods for Solving Problems Week 02 Quiz Answers

Quiz 1: Computers and Logic

Q1. Among Polya’s problem-solving heuristics is the suggestion “Look for a related problem that you know.” Why might this be an interesting or challenging suggestion for a computational problem-solving system?

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Pursuing this heuristic would involve tackling the notion of similarities or analogies between various (superficially distinct) problems. This would be an interesting research project!

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Q2. The “rotating-quarters” problem is difficult to approach via the same methods as (say) Rubik’s Cube. Which of the following reasons is most relevant to this difficulty?

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Finding a solution appears to involve elements of mental imagery or mental simulation.

Q3. The “Teddy Roosevelt” problem is difficult to approach via the same methods as Rubik’s Cube. Which of the following reasons is most relevant to this difficulty?

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There is a potentially (extremely) wide range of real-world or common-sense knowledge involved in answering the question; so the problem is not self-contained as many puzzles are.

Q4. Consider the “10 coins in three cups” problem given at: https\://curiosity.com/topics/can-you-solve-the-3-cups-10-coins-logic-puzzle-curiosity

What might make this difficult to solve with a computational system?

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A “standard” search program assumes a particular representation of the problem, while this particular problem involves finding a creative reconsideration of the problem statement itself.

Q5. Consider the “monkey climbing a rope” problem given at:

https\://activityworkshop.net/puzzlesgames/monkey/index.html

What makes this problem difficult?

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The problem involves elements of physics knowledge and (most likely) mental simulation and imagery.

Q6. Consider the “sand timers” problem (Problem 4) at the following website: https\://www.analyticsvidhya.com/blog/2016/07/20-challenging-job-interview-puzzles-which-every-analyst-solve-at-least

What can you say about this problem?

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This problem involves an unavoidable degree of probability or uncertainty in its solution.

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Q7. Consider the following propositional logic statements:

  • IF (P AND Q) THEN R
  • P AND S
  • Q AND V

Which of the following statements cannot be derived from these three statements?

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(NOT P) OR (NOT Q)

Q8. Consider the hammerhead shark. Why do you think the animal evolved this sort of head shape?

https\://www.nationalgeographic.com/content/dam/animals/thumbs/rights-exempt/fish/group/hammerhead-sharks_thumb.ngsversion.1498159813652.adapt.1900.1.jpg

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Presumably the distance between the two eyes helps with binocular vision (particularly for points in the region between the two eyes).

Q9. Why do we need to use a toroid shape in the Schelling model of neighborhoods as discussed in the lecture?

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A toroid allows all individuals to have exactly 8 neighbors, otherwise the corner location cannot possibly have 4 neighbors.

Q10. What does this photograph suggest about the difficulty of the “vision” problem?

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Vision, because it involves all sorts of guesswork and heuristics in interpreting three dimensions from a two-dimensional projection, is capable of being confused or misled by certain images

Methods for Solving Problems Week 03 Quiz Answers

Quiz 1: Judgment and Decision Making

Q1. In the Kahneman and Tversky paper, which feature of human valuation is most relevant to the $300 bonus scenario?

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People’s valuation function is asymmetric, placing a greater relative weight on loss than on gain.

Q2. Which of these sentences, referring to the distinction between judgment and problem solving, is not true?

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People are in general exceptionally good at both problem-solving and judgment tasks.

Quiz 2: Heuristics and Biases

Q1. Let’s see if you can recognize another (famous) example of the “conjunction fallacy”. Here’s a description of Linda: Linda is thirty-one years old, single, outspoken, and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in antinuclear demonstrations. Here are your choices – your job is to rank order them in terms of probability:

  • Linda is a teacher in an elementary school.
  • Linda works in a bookstore and takes yoga classes.
  • Linda is active in the feminist movement.
  • Linda is a psychiatric social worker.
  • Linda is a member of the League of Women Voters.
  • Linda is a bank teller.
  • Linda is an insurance salesperson.
  • Linda is a bank teller and is active in the feminist movement.

Which of these statements is true?​

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Linda is more likely to be a bank teller than a bank teller who is active in the feminist movement.

Linda is more likely to be a bank teller active in the feminist movement than a bank teller.

Linda is most likely to be a teacher.

There is no conclusion to be drawn from these choices.

Q2. The “decouple-the-metal-rings” problem is difficult to approach via the same methods as (say) Rubik’s Cube. Which of the following reasons is most relevant to this difficulty?

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It is hard to know, on inspection, what constitute the distinct “states” of the problem space.

Q3. In fuzzy logic, it is possible to speak of “degrees of truth” using real numbers between 0 and 1. (Here, 0 corresponds to “false” and 1 to “true”.) Thus, we might say that the statement “The 2018 Boston Red Sox are a good baseball team” is “0.98 true” (i.e., close to certain) and “The 2018 Baltimore Orioles are a good baseball team” is “0.02 true” (i.e., very close to certainly false). Which of these statements – none of which is entirely true or false — is most true?

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February is a cold month in Boulder.

Methods for Solving Problems Week 04 Quiz Answers

Quiz 1: Regression to the Mean

Q1. Suppose Mike is playing a coin game as follows. First he throws three fair coins into the air (First Toss). For each “heads”, he wins a dollar. Then, he tosses the three coins again (Second Toss). For each “heads” on this second toss, he also wins a dollar. (So he can win anywhere from $0 to $6 in one play of the game.)

What is the probability of tossing three heads on the first toss? (To three decimal places)

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probability of tossing three heads on the first toss is 0.125.

Q2. What is the probability of tossing fewer than 3 heads on the first toss? (To three decimal places)

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probability of tossing fewer than 3 heads on the first toss is 0.875.

Q3. What is the probability of tossing 0 heads on the first toss? (To three decimal places)

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probability of tossing 0 heads on the first toss is 0.125.

Q4. Suppose Mike tosses 0 heads on the first toss. What is the probability of doing better than that on the second toss? (To three decimal places)

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probability of doing better than 0 heads on the second toss, given 0 heads on the first toss, is 0.875.

Q5. Suppose Mike tosses 0 heads on the first toss and then curses the coins (“You stupid coins!”) What is the probability of doing better on the second toss? (To three decimal places)

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probability of doing better on the second toss after tossing 0 heads on the first toss is still 0.875, regardless of his comments

Q6. Suppose Mike tosses 3 heads on the first toss. What is the probability of doing worse than that on the second toss? (To three decimal places)

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probability of doing worse than 3 heads on the second toss, given 3 heads on the first toss, is 0.875.
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Q7. Suppose Mike tosses 3 heads on the first toss, and then praises the coins (“Good coins!”) What is the probability of doing worse on the second toss? (To three decimal places)

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probability of doing worse on the second toss after tossing 3 heads on the first toss is still 0.875, regardless of his comments.

Q8. Explain why these answers might lead Mike to (mistakenly) believe that criticizing the coins helps change their behavior in the right way, but praising the coins isn’t a good idea.

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Mike’s belief that criticizing the coins helps change their behavior is based on a cognitive bias known as the “illusion of control” or “superstition fallacy.” People often believe that their actions, like criticizing or praising, can influence random events like coin tosses, even though these actions have no real impact on the outcomes. This mistaken belief can lead to reinforcing certain behaviors, even though they are not logically connected to the outcomes.

In reality, coin tosses are random events, and the outcomes are not influenced by comments or actions. Both criticizing and praising the coins have no effect on the probabilities of the coin tosses. Therefore, any observed patterns in the outcomes are purely coincidental, and Mike’s actions do not change the behavior of the coins.

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Quiz 2: Small Numbers Fallacy

Q1. Suppose you toss 4 coins. What is the probability of getting 0 heads? What is the probability of getting 0 tails?

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probability of getting 0 heads is 0.0625, and the probability of getting 0 tails (all heads) is also 0.0625. 
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Q2. Now, suppose you toss 100 coins. What is the probability of getting 0 heads? Or 0 tails?

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When tossing 100 fair coins, the probability of getting either 0 heads or 0 tails is extremely low. In fact, it’s so close to zero that it’s practically impossible to calculate manually. The probability is a very small decimal number, and it’s not feasible to express it accurately without using specialized mathematical software or calculators.

In general, with a large number of coin tosses, the probability of getting all heads or all tails becomes exponentially smaller as the number of tosses increases. It approaches zero but never quite reaches it.

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