Core Chapter 10: Probability

Question 1

Define probability and state the probability of impossible, certain and all other events

Answer 1

Probability: chance of an event occurring
- Impossible events: 0
- Certain events: 1
- All other events: 0-1

Question 2

Define:
- Number of trials
- Outcomes
- Frequency
- Relative frequency

Answer 2

• Number of trials: no. of times experiment is performed
• Outcomes: different possible results for 1 trial of the experiment
• Frequency: no. of times outcome has been observed
• Relative frequency:
  frequency of outcomes/no. of trials
  (experimental probability)

Question 3

Define
- Sample space (u)
- Events
- Complementary events

Answer 3

• Sample space (u): set of all possible outcomes of an experiment
• Events: set of outcomes in the sample space that have a particular property (elements of u)
• Complementary events: one of the events must occur

P(A) + P(A’) = 1

Question 4

Determine theoretical probability

Answer 4

P(A) = n(A)/n(U)
(if all outcomes are equally likely to occur)

Question 5

Apply the addition law of probability to determine the probability of compound events

Answer 5

• Compound events: when there is more than 1 event in the sample space

Event that both A and B occur: A∩B
Event that A or B occur/both occur: A∪B

A∪B = P(A) + P(B) - P(A∩B)
A∪B = P(A) + P(B)
(*If A and B are disjointed mutually exclusive events and P(A∩B) = 0 )

Question 6

Define independent events

Answer 6

Independent events: if the occurrence of each event does not affect the occurrence of the other

P(A∩B) = P(A) x P(B)

Question 7

Define dependent events

Answer 7

Dependent events: if occurrence of 1 event affects the occurrence of the other event
(sampling experiments without replacement)

P(A∩B) = P(A) x P(B given that A has occurred)

Question 8

Define conditional probability

Answer 8

Conditional probability: probability of 1 event given that another event has already occurred

P(A|B) = P(A∩B)/P(B)