Elementary outcome
One possible outcome of the probability experiment
ex.: heart 6 ( in a deck )
Sample space
Set of all possible elementary outcomes
ex. : when tossing a coin only 2 outcomes are possible in the SS
ex. : all cards in a deck
Event
An outcome or set of outcomes of a random phenomenon
- -> every event is an elementary outcome but not other way round
ex. : heart card ( in a deck), so subset of the SS
Disjoint
Dependent
–> one event influences the other
“when A happens, B can’t” , thus the 2 events have no outcome in common and so can never occur together
ADDITION RULE (or)
Not Disjoint/Joint
Independent
–> one event doesn’t influence the outcome of the other
MULTIPLICATION RULE (and)
Probability range
Number between 0 and 1
0≤ P(A) ≤1
Complement rule
Finding out what the probability is that an event doesn’t occur
P(A) = 1-P(𝐴𝐶)
ex. : Probability that treatment is effective is 30%
- -> 1-0.3=0.7
Random phenomenon
Refers to outcomes that we cannot predict but that nonetheless have a regular distribution in very many distributions
Probability
Refers to the proportion of times the event occurs in many repeated trials of a random phenomenon
Trials are independent if …
the outcome of one trial doesn’t influence the outcome of any other trial
P(A and B) = P(A) x P(B)
MULTIPLICATION RULE
Random variable
Refers to a variable whose value is a numerical outcome of a random process
–> its distribution can be discrete vs continuous
Probability distribution
Indicates what the possible values of X are + how probabilities are assigned to those values
–> can be described by a density curve
Continuous random variable
Refers to a variable whose value is obtained by measuring
–> probability that X is between an interval of numbers is the area under the density curve
ex.: height of students in class, weight of students in class
Discrete random variable
Refers to a variable whose value is obtained by counting
ex.: number of students present, number of red marbles in a jar
–> X has a countable number of possible values (Probability histogram)
Density curve
Describes the probability distribution of a continuous random variable
–> probability of any event is the area above or below the curve
Normal distribution
Is a type of continuous probability distribution
Expected value
Refers to a predicted value of a variable, calculated as the sum of all possible values each multiplied by the probability of its occurrence
Conditional probability
P(B given A) = P(A and B) x P (A)