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Measuring uncertainty

Measuring uncertainty

1.[2p]

What is the fatal objection to defining probability as favourable cases over total cases?

Correct
The answer is: "Equally possible" already means "equally probable", so the definition uses the word it defines
The answer is: "Equally possible" already means "equally probable", so the definition uses the word it defines
The answer is: "Equally possible" already means "equally probable", so the definition uses the word it defines

2.[2p]

Two fair dice are rolled. What is the probability that the total is 8? Give the answer to three decimal places.

CorrectNot quite: 0.139

3.[3p]

What is the probability of at least one six in four rolls of a fair die? Give the answer to four decimal places.

CorrectNot quite: 0.5177

4.[3p]

What is the probability of at least one double six in twenty-four rolls of a pair of fair dice? Give the answer to four decimal places.

CorrectNot quite: 0.4914

5.[2p]

In Kerrich's record the number of heads got further from half the number of tosses as the experiment went on, while the fraction of heads got closer to 0.5.

Correct
The answer is: True

6.[2p]

Why does no finite record of coin tosses define the probability of heads?

Correct
The answer is: A finite record gives a fraction, never a limit, and the limit is what was claimed
The answer is: A finite record gives a fraction, never a limit, and the limit is what was claimed
The answer is: A finite record gives a fraction, never a limit, and the limit is what was claimed

7.[1p]

A bookmaker quotes 4 to 1 against. What probability does that price imply?

CorrectNot quite: 0.2

8.[3p]

Which of these are agreed on by the frequency reading and the degree of belief reading?

Select all that apply

Correct
Correct
Correct
The answer is: Every probability lies between $0$ and $1$, Mutually exclusive alternatives that exhaust the possibilities have probabilities summing to $1$, For disjoint events, the probability of either one is the sum of the two

9.[2p]

Match each name to what they contributed.

  • Cardano

  • Laplace

  • Kerrich

  • Kolmogorov

  • the classical definition with equally possible cases

  • ten thousand recorded coin tosses

  • probability as axioms rather than a meaning

  • the first written rule for counting cases

Show the answer

Cardano: the first written rule for counting cases Laplace: the classical definition with equally possible cases Kerrich: ten thousand recorded coin tosses Kolmogorov: probability as axioms rather than a meaning