Chapter 5 Flashcards
Probability
The way we quantify uncertainty. If we perform many trials, the probability of an event is the proportion of those trials for which it is the outcome. Refers to long run observations.
Random process
Some process or procedure the outcome of which is not known definitively.
Trial
One iteration of a random process
Event
An outcome of a random process
Law of large numbers
As the number of trials increases, the observed proportions of outcomes constituting each event approaches their true probabilities.
What are the properties of probability
i. All probabilities are between 0 and 1
ii. The probabilities of all events from a random process must sum up to 1.
iii. The complement rule
Iv. The addition Rule
vi. The multiplication rule.
The complement Rule
The probablilites of an event not occurring is 1 - [the probability of that event occurs]. P(A^c) = 1 – P(A)
The addition rule
The probability of A or B is the sum of the two probabilities minus the probability of both. P(A or B)= P(A)- P(B)-P(A and B)
The muiltiplication rule
In the events A and B are independent, then the probability of A and B occurring is the product of their probabilities; P(A and B)= P(A) *P(B)
Conditional Probability
What is the probability A occurs if another event b occurs.
Conditional Probability Formula
P[A|B]= P[AvB]/P(B)
Independent
Two events are independent if the occurence of one event has no influence on the occurrence of the other event. Ex: rolling a 5 on a dice doesn’t make rolling a 5 on the nice dice less likely.
How can we say if two events are independent
If P[A|B]=P(A) and P[B|A]=P(B)
Random Phenomena
Everyday choices for which the outcome is uncertain.
Phenomena
Any observable occdurence.
