conditional probability (y2)

independent events

events that are unaffected by eachothers' outcomes

non-independent events

events where one's probability is affected by the outcome of the other

mutually exclusive events

events that cannot both occur

n(X)

indicates the number of outcomes that fulfil X

i.e. if there are 3 yellow dice in a bag of dice, and A means that a yellow dice will be picked at random, n(A) = 3

∅

empty set, denotes no possible outcomes i.e. 𝐴∩𝐵 = ∅ if A and B are mutually exclusive

probability formulae

the probability of event A given event B has already occured is denoted as P(A|B)

P(A|B) = P(A∩B)/P(B)

P(A∪B) = P(A) + P(B) - P(A∩B)

expressing conditional probability graphically

conditional probabilities can be drawn as tree diagrams, where the second set of branches denotes the event dependent on the outcome of the other