Week 8

Question 1

What is the paradox of change in relation to identity? -

Answer 1

It suggests that when something changes it becomes a different object.

Question 2

What is the key distinction between an object and its properties in logic? -

Answer 2

Objects remain the same while their properties can change.

Question 3

How does Leibniz’s Law apply to identity? -

Answer 3

If two objects are identical they must share all the same properties.

Question 4

In the context of probability what does a probability of 0 represent? -

Answer 4

Certainty that an event will not occur.

Question 5

What is the role of the reference class in statistical reasoning? -

Answer 5

It determines the specific group used to calculate probabilities.

Question 6

How is the conjunction of two probabilities calculated? -

Answer 6

By multiplying the probabilities of each event happening together.

Question 7

Which of the following is an example of conditional probability? -

Answer 7

The probability that it will rain tomorrow given that it rained today.

Question 8

What is the relationship between inductive reasoning and probability? -

Answer 8

Inductive reasoning deals with likelihoods and probabilities not certainties.

Question 9

The following set of statistics was collected from ten people.
If r is a randomly chosen person in this collection, assess the inductive validity of the following inference: r is tall and wealthy; so r is happy.
Let: t be ‘r is tall’. w be ‘r is wealthy’. h be ‘r is happy’.

Answer 9

The inference is valid.

For there are three people who are tall and wealthy, and two of them are happy.

Question 10

Suppose there are two illnesses, A and B, that have exactly the same observable symptoms: 90% of those who present with the symptoms have illness A; the other 10% have illness B. Suppose, also, that there is a pathology test to distinguish between A and B. The test gives the correct answer 9 times out of 10. What is the probability that the test, when applied to a randomly chosen person with the symptoms, will say that they have illness B? (Hint: consider a typical sample of 100 people with the symptoms, and work out how many the test will say to have illness B.)

Answer 10

90 will have illness A, and 10 will have illness B.

Since the test gives the correct result 9 times out of 10, it will say that 81 of the 90 have A (90 × 9/10), and 9 of them have B.

Of the 10 with illness B, it will say that 9 have illness B and 1 has illness A.

Hence a total of 18 will be said to have B, and so the probability of a (randomly chosen) person being shown to have B is 18/100.