Topic 3 - Probability

Question 1

What is a random experiment?

Answer 1

The process of observing something uncertain

For instance, when we toss a coin the outcome is uncertain and hence, it can be considered a random experiment

Question 2

What is an outcome?

Answer 2

Result of a random experiment

Question 3

What is Sample space S?

Answer 3

The set of all possible outcomes of a random experiment

For example in the case of tossing a coin the sample space S is 2 as there are only 2 possible outcomes (heads or tails) whereas when rolling a dice the sample space S is 6 as there are 6 different possibilities of outcomes

Question 4

What is Event A?

Answer 4

A subset of the sample space S

We say that A occurred, if the actual outcome of the experiment is in A

For example an event in rolling a dice may be getting an even number or getting a number greater than 5 whereas when tossing a coin an event may be getting heads or another event may be getting tails

Question 5

What do A and B signify when used as labels for 2 Venn diagrams?

Answer 5

A and B are 2 events in a sample space S

Question 6

What does A ∩ B mean?

Answer 6

A inverted U B means A intersection B

It is the set of all outcomes in sample space S that belong to both A and B (middle overlap of Venn diagrams)

Question 7

What does it mean if events A and B have no intersection?

Answer 7

Then events A and B are mutually exclusive

Question 8

Wha are mutually exclusive events?

Answer 8

A and B are Mutually Exclusive Events if they have no basic outcomes in common i.e., the set A ∩ B is empty (no overlap of circles- 2 separate instead)

Question 9

What does A U B mean?

Answer 9

Translates to A union B

If A and B are two events in a sample space S, then the union, A U B, is the set of all outcomes in S that belong to either A or B
(A and B circles as well as overlap shaded)

Question 10

What are collectively exhaustive events?

Answer 10

Events E1, E2, … Ek are Collectively Exhaustive events if: E1 U E2 U . . . U Ek = S

If the union of events E1 E2 and so on equal the space space S (all possible outcomes)
i.e., the events completely cover the sample space

Question 11

What is the complement of an event?

Answer 11

The Complement of an event A is the set of all basic outcomes in the sample space that do not belong to A

Basically all the area outside the Venn diagram circle A- outer square highlighted

Question 12

How is the complement of event A denoted?

Answer 12

Denoted by A bar (A with horizontal line on top)

Question 13

What does the union of A and A bar give you?

Answer 13

A U A bar is equal to sample space S

Question 14

What is probability and what do different probabilities mean?

Answer 14

It is a measure of the likelihood that an uncertain event will occur (always between 0 and 1)

0 means that it is impossible that an event will occur whereas means that an event will certainly occur

Question 15

What is the range of probability?

Answer 15

For any event probability will be from 0 to 1

Question 16

How many ways/approaches are there to assess the probability of an uncertain event?

Answer 16

3 approaches/ways

Question 17

What are the ways/approaches to assess the probability of an uncertain event?

Answer 17

1) Classical probability
2) Relative frequency probability
3) Subjective probability

Question 18

What is the classical probability method to assess the probability of an uncertain event and when it is appropriate?

Answer 18

Classical method of assigning probabilities is appropriate when all outcomes in the sample space are equally likely to occur (e.g. rolling a dice)

Question 19

What is the relative frequency probability method to assess the probability of an uncertain event?

Answer 19

The limit of the proportion of times that an event A occurs in a large number of trials, n

Question 20

What is the subjective probability method to assess the probability of an uncertain event?

Answer 20

An individual opinion or belief about the probability of occurrence (e.g. probability Southampton winning the Premiership)