#14.1
Be able to calculate the probability of an event.
Using modelling assumptions such as equally likely outcomes.
Notation: P(A)
#14.2
Understand the concept of a complementary event and know that the probability of an event may be found by means of finding that of its complementary event.
Notation: \(A'\) is the event “not-\(A\)”.
#14.3
Be able to calculate the expected frequency of an event given its probability.
Notation: Expected frequency \(= nP(A)\)
#14.4
Be able to use appropriate diagrams to assist in the calculation of probabilities.
E.g. tree diagrams, sample space diagrams, Venn diagrams.
#14.5
Understand and use mutually exclusive events and independent events.
#14.6
Know to add probabilities for mutually exclusive events.
E.g. to find \(P(A~or~B)\) .
#14.7
Know to multiply probabilities for independent events.
E.g. to find \(P(A~and~B)\).
Including the use of complementary events, e.g. finding the probability of at least one 6 in five throws of a dice.
#14.8
Understand and use mutually exclusive events and independent events and associated notation and definitions.
For mutually exclusive events \(P(A ∩ B) = 0\) for any pair of events.
#14.9
Be able to use Venn diagrams to assist in the calculations of probabilities. Know how to calculate probabilities for two events which are not mutually exclusive.
Venn diagrams for up to three events.
Learners should understand the relation:
\(P(A ∪ B) = P(A) + P(B) - P(A ∩ B)\).
[Excludes: Probability of a general or infinite number of events. Formal proofs.]
#14.10
Be able to calculate conditional probabilities by formula, from tree diagrams, two-way tables, Venn diagrams or sample space diagrams.
\(P(A|B) = \dfrac{P(A∩B)}{P(B)} \)
[Excludes: Finding reverse conditional probability i.e. calculating \(P(B|A)\) given \(P(A|B)\) and additional information.]
#14.11
Know that \(P(B|A) = P(B) \iff B\) and \(A\) are independent.
In this case \(P(A ∩ B) = P(A)⋅P(B)\).