Probability Flashcards
What is a probability? Random trial?
Probability: The probability of an event is the proportion of times the event occurs if we repeat a random trial over and over again under the same conditions.
Random Trial: A random trial is a process or experiment that has two or more possible outcomes whose occurrence cannot be predicted with certainty.
What does ‘mutually exclusive’ mean?
Two events cannot occur at the same time
What is the Addition Rule for Probabilities and how do you use it? -> Mutually exclusive
Two events (A and B) are mutually exclusive if they cannot both occur (i.e., Pr[A and B]=0).
If A and B are mutually exclusive, then the probability of A or B occurring is the sum of the probability of A occurring and the probability of B occurring (i.e., Pr[A or B]=Pr[A]+Pr[B]).
What is a probability distribution?
A probability distribution describes the probabilities of all possible outcomes of a random trial.
What does it mean if events are independent?
Two events are independent if knowing one outcome gives no information about the other outcome. More formally, A and B are independent if Pr[A and B]=Pr[A]Pr[B].
What is the General Multiplication Rule and how to do you use it?
Independent: Pr[A and B]=Pr[A]Pr[B]
Dependent: Pr[A and B]=Pr[A]Pr[B|A]
What is the Law of Total Probability and how do you use it?
The law of total probability, Pr[A]=ΣPr[B] Pr[A|B], makes it possible to calculate the probability of an event (A) from all of the conditional probabilities of that event.
The law multiplies, for all possible conditions (B), the probability of that condition (Pr[B]) times the conditional probability of the event assuming that condition (Pr[A|B])
What is the general addition rule? -> Not mutually exclusive
The general addition rule gives the probability of either of two events occurring when the events are not mutually exclusive:
Pr[A or B]=Pr[A]+Pr[B]−Pr[A and B].
The general addition rule reduces to the addition rule when A and B are mutually exclusive, because then Pr[A and B]=0.
What does it mean if events are dependent?
Events are not independent. The occurrence of one event affects the occurrence of another event.
Pr[A and B]=Pr[A]Pr[B|A].
Conditional probability
The conditional probability of an event is the probability of that event occurring given some condition.
Equations to work out P[A|B]
P[A|B]= P[A and B] / P[B]
P[A|B]= P[B|A] P[A] / P[B] (B theorem)
Key things to remember
If calculating probability of two events make sure to calculate P in both directions and then add up (e.g. P have A and C nucleotides -> P(AC) + P(CA)
When thinking about conditional probabilities and using probability tree think very carefully about whether data is giving you the conditional data or not -> when false positive etc data it tends to be (e.g. the number of HIV +ve tests for HIV negative people)
For Bayes theory the one you are trying to calculate is like the probability of having smoked if you get cancer -> it is going backwards
