5. Probability Flashcards
Proportion
fraction of individuals having a particular attribute. *Can range from 0 to 1
Probability
Probability of an event is it’s true relative frequency, or proportion of times the event would occur if repeated over and over again an infinite number of times
Probability of event A written as Pr(A)
Probability Distribution
the true relative frequency of all possible values of a random variable
Mutually exclusive
the relationship between two events where they cannot both be true (ex when rolling a 6 sided die, it could land on any number from 1-6 but not more than one at once)
Equation for probability of two events (A and B) which are mutually exclusive occuring together
Pr(A and B) = 0
equation for probability of two events (A and B) which are NOT mutually exclussive occuring tgth
Pr(A and B) NOT = 0
The addition principle
if two events (A and B) are mutually exclusive, the Pr[A OR B] = Pr[A] + Pr[B]
Probability of a range of values
apply the addition principle (ex Pr[number of green M&Ms > 6]
Sum of all mutually exclusive probabilities
= 1
Probability of something NOT happening
Pr[NOT event A] = 1 - Pr[A]
GENERAL Addition Principle
If areas are NOT mutually exclusive and you want probability of either A or B, must subtract area where it could be both A or B
ex Pr[A or B] = Pr[A] + Pr[B] - Pr[A AND B]
Independance
Two events are independent if occurrence of one gives no information about whether the second will occur
Multiplication Principle
If two events (A and B) are independent, than:
Pr[A AND B] = Pr[A] x Pr[B]
**Only true when condition of independence is met
Probability Tree
Visual representation of multiplication principle
Dependent events
Probability of one event may depend on the outcome of another event
How could you mathematically show that results are NOT independent/ ARE independent?
Determine if the multiplication principle describes the data, if NOT events or NOT independent.
Ex. determine probability of A and B using a Probability tree, then try and calculate probability of A and B using multiplication principle. If not equal, not independent
Conditional probability
cond. prob of an event is the probability of that event occurring given a condition is met.
written as Pr[X | Y], read as probability of X given Y OR Y is true, thus what is the probability of X
Law of total probability
Pr[X] = Sum for all values of Y Pr[X|Y] * Pr[Y]
GENERAL Multiplication Rule
Applies to dependent events, with conditional probability
Pr[A AND B] = Pr[A]Pr[B | A]
If events are independent, Pr[B|A] = Pr[B]
Pr[A AND B] = Pr[A]Pr[B | A]
EQUAL TO
Pr[A AND B] = Pr[B]Pr[A | B]
THEREFORE
Pr[B]Pr[A | B] = Pr[A]Pr[B | A]
