Probability Flashcards
Experiment definition
Repeatable process that gives rise to a number of different outcomes
Event definition
Collection of outcomes
Sample space definition
The set of all possible outcomes
What does A’N’B mean
The intersection - A and B
What does A’U’B mean
The union - A or B or both
What does n(A) mean?
The number of outcomes in the event A
What does P(A) mean?
The probability of A occurring
Independent events definition
When one event has no effect on the other
Equation used to prove if two events are independent
P (A’N’B) = P(A) x P(B)
Mutually exclusive events definition
When events have no common outcomes
Equation used to prove if two events are mutually exclusive
P(A’N’B) = 0 (ie no cross over in Venn diagram)
P(A’U’B) = P(A) + P(B)
When are tree diagrams used?
To show the outcome of two or more events happening in succession
IE picking counters out of a bag one after each other
What is conditional probability?
When the probability of an event depends on the outcome of the previous event
Notation of conditional probability
P(B|A)
Probability of B given A has already occurred
Formula for conditional probability
P(B|A) = P(B’N’A) / P(A)
Addition formula
P(AUB) = P(A) + P(B) - P(A’N’B)
Multiplication rule for conditional probability
P(A’N’B) = P(B|A) x P(A)
Random variable definition
A variable whose value depends on the outcome of an event
Discrete variable
A variable that can only take a possible set of outcomes
IE an integer, not continuous
Probability distribution definition
the probability of every outcome in the sample space
Displayed as a table or a probability mass function
Discrete uniform distribution definition
A distribution where the probabilities of each outcome is the same
IE a fair dice, all number are 1/6th likely to come up
