Lesson test: Measuring uncertainty

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Measuring uncertainty

1.[2p]
What is the fatal objection to defining probability as favourable cases over total cases?

"Equally possible" already means "equally probable", so the definition uses the word it defines

Correct

It gives the wrong answer for dice

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

It cannot handle more than two outcomes

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

It requires the cases to be infinite in number

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 $0.5$ .

True

Correct

False

The answer is: True

6.[2p]
Why does no finite record of coin tosses define the probability of heads?

A finite record gives a fraction, never a limit, and the limit is what was claimed

Correct

Coins are never fair enough to measure

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

Because the tosses are not independent

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

Because the fraction is always exactly one half

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

Every probability lies between $0$ and $1$

Correct

Mutually exclusive alternatives that exhaust the possibilities have probabilities summing to $1$

Correct

For disjoint events, the probability of either one is the sum of the two

Correct

A probability may be assigned to a single unrepeatable event

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

1.[2p] What is the fatal objection to defining probability as favourable cases over total cases?

2.[2p] Two fair dice are rolled. What is the probability that the total is 8? Give the answer to three decimal places.

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.

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.

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.

6.[2p] Why does no finite record of coin tosses define the probability of heads?

7.[1p] A bookmaker quotes 4 to 1 against. What probability does that price imply?

8.[3p] Which of these are agreed on by the frequency reading and the degree of belief reading?

9.[2p] Match each name to what they contributed.

1.[2p]
What is the fatal objection to defining probability as favourable cases over total cases?

2.[2p]
Two fair dice are rolled. What is the probability that the total is $8$ ? Give the answer to three decimal places.

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.

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.

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 $0.5$ .

6.[2p]
Why does no finite record of coin tosses define the probability of heads?

7.[1p]
A bookmaker quotes $4$ to $1$ against. What probability does that price imply?

8.[3p]
Which of these are agreed on by the frequency reading and the degree of belief reading?

9.[2p]
Match each name to what they contributed.