Exam 10: Inductive Logic

B and ~B are mutually exclusive.

In an argument by analogy, the more relevant dissimilarities there are between the objects being compared, the less likely the conclusion is to be true.

Suppose that P(h) = 3/5, P(e/h) = 2/5, and P(e/~h) = 3/5. Bayes' theorem reveals that

Symbols list Where necessary, you may use the list below to copy-and-paste symbols into your answer. →;↔;•;~;⋁;\;≠;$;× You have an ordinary deck of cards. You draw one card, do not replace it, and then draw a second card. Each series of draws begins with a full deck. Assuming you are as likely to draw one card as another, find the following probability: P(drawing a diamond • drawing a spade)

The general rule of disjunction applies to any pair of statements.

Use the rules of probability to determine the strength of the following argument. In other words, given that the premises are true, how likely is the conclusion? Northern and Southern are in different brackets for the semifinals. Odds are 4 to 7 that Northern will win its semifinal game, and 5-to-3 that Southern will win its semifinal game. So, Northern is certain to be playing Southern in the final game.

Identify the hypothesis in the following argument; and, if it fails to meet the four criteria for good scientific hypotheses, state which criterion is violated, and explain your answer. Patricia noticed that every time she set something on her kitchen counter, it ended up on the floor next to the cat. First she noticed this happened with a pencil, and then a marble. She thought it might be that the counter was sloped and round things rolled off, but then it happened to one of her cat's square catnip toys. She concluded that her dog was trying to get the cat in trouble.

Symbols list Where necessary, you may use the list below to copy-and-paste symbols into your answer. →;↔;•;~;⋁;\;≠;$;× You have an ordinary deck of cards. You draw one card, do not replace it, and then draw a second card. Each series of draws begins with a full deck. Assuming you are as likely to draw one card as another, find the following probability: P(drawing a jack and drawing a queen on two consecutive draws, in either order)

In the following induction by enumeration, identify the sample and the population, and discuss the appropriateness of sample size and method of surveying. A random, nationwide telephone survey of 2,600 people asked if the respondents had ever committed a felony that had gone undetected. Less than 2 percent said yes. Consequently, over 98 percent of the felonies committed are detected.

The fallacy of incomplete evidence is committed in an argument from authority when the authority cited is not infallible.

Identify the hypothesis in the following argument; and, if it fails to meet the four criteria for good scientific hypotheses, state which criterion is violated, and explain your answer. Nathan has been having problems with his computer. Occasionally it locks up and will not respond to any commands from the keyboard, and it doesn't seem to matter what program he is running at the time. Although the error message he receives indicates a problem with memory, he concludes that the evil Microsoft Corporation is attempting to establish a monopoly by crashing any non-Microsoft programs.

Which of Mill's Methods is illustrated in the following passage? If, in your opinion, the conclusion reached indicates that an inadequate hypothesis was employed, explain why and formulate a better hypothesis. Nettie's car flunked the VET test in Louisville with carbon emissions of 25, 000 parts per million. After replacing the muffler and tailpipe, Nettie had her car retested and it passed-this time with carbon emissions of only 2,500 parts per million, well within the range of emissions for the normal operation of a car. On the basis of this experience, Nettie decided to have her muffler and tailpipe checked before each VET test in the future.

Use the rules of probability to determine the strength of the following argument. In other words, given that the premises are true, how likely is the conclusion? The odds are 2 to 1 that Archarcharch will win the Kentucky Derby, but odds are 3 to 2 that Archarcharch will win the Preakness. So, odds are that Archarcharch will not win both the Kentucky Derby and the Preakness. (Note: The Derby and the Preakness are independent races.)

The fallacy of incomplete evidence arises in inductions by enumeration when the sample is too small or is biased.

A confirming instance of a hypothesis is

A cause is a necessary condition for an event if its presence is enough to bring about the event.

Symbols list Where necessary, you may use the list below to copy-and-paste symbols into your answer. →;↔;•;~;⋁;\;≠;$;× You have an ordinary deck of cards. You draw one card, do not replace it, and then draw a second card. Each series of draws begins with a full deck. Assuming you are as likely to draw one card as another, find the following probability: P(drawing hearts on first draw • drawing hearts on second draw)

Symbols list Where necessary, you may use the list below to copy-and-paste symbols into your answer. →;↔;•;~;⋁;\;≠;$;× You have an ordinary deck of cards. You draw one card, do not replace it, and then draw a second card. Each series of draws begins with a full deck. Assuming you are as likely to draw one card as another, find the following probability: P(drawing eights on two consecutive draws)

Suppose that P(h/e) = 5/9. Then P(~h/e) is

The probability of A • ~A is greater than zero.