1. Using the material you’ve learned so far and the reading “Inductive Reasoning
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Question
1. Using the material you’ve learned so far and the reading “Inductive Reasoning – Part 1,” explain the difference between a sound argument and a cogent argument. Give an example of each.
2. To the best of your ability, explain the difference between “certainty” and “objectively probable.” Give examples.
3. Explain the difference between probabilities and statistics and how one is used to inform the other. Give examples.
4. In your own words, explain the difference between inductive and deductive logic.
5. Using the video, “Why Probability is Important,” list five reasons to study probability theory. Choose two of these reasons and explain why each is either a compelling reason for you or not a compelling reason for you.
6. To the best of your ability, explain the difference between the classical and logical interpretations of probability.
7. In your own words and to the best of your ability, explain a significant problem for the classical interpretation of probability. (I am not looking for a technical, mathematical answer here. Feel free to explain the problem in informal terms using examples if you need to.)
8. Using the video, “Probability – The Logical Interpretation,” explain the concept of conditional probability.
9. In your own words, what is the benefit of the frequency interpretation of probability over the other two covered in this unit?
10. Choose one of the objections to the frequency interpretation of probability and explain it in your own words.
Explanation / Answer
(1). A valid deductive argument with a true premise is called a sound argument, i.e., a sound argument is a valid argument whose conclusion follows from its premise and the premise of which is true.
A strong inductive argument with a set of likely-to-be-true premise is referred to as a cogent argument.
(3). The problems taken up by probability and statistics are inverse to each other. In probability theory, we reflect upon some causal process which has some randomness or uncertainty, and we find out what happens. In statistics we observe something that has already happened and try to outline what underlying process would explain those observations.
(4). Inductive reasoning moves from specific instances into a generalized conclusion while deductive reasoning moves from generalized principles that are known to be true to a specific conclusion.
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