Probability concept Flashcards
Mutually exclusive
only one event can occur at a time.
Exhaustive
the events cover all possible outcomes.
Subjective Probability
Make a personal assessment of probability without reference to any particular data.
Objective Probability
▪️ Empirical Probability
estimate the probability of an event based on historical data.
▪️ Priori Probability
Based on logical analysis such as binomial probability function
Odd ratio
event will occur / event will not occur
Ex: 0.25 probability for winning and 0.75 for losing. Odds for winning = 0.25/0.75 = 0.33
Odds for E
P(E) / 1 - P(E)
Given odds for E of a to b
a / (a+b)
Odds against E
1 - P(E) / P(E)
Given odds against E of a to b
b / a + b
Conditional Probability
The probability of A given that B has occurred
P(A|B) = P(AB) / P(B)
thus
P(AB) = P(A|B)P(B)
Addition Rule of Probability
The probability that A or B occurs or both occur
P(A or B) = P(A) + P(B) - P(AB)
Multiplication Rule of Probability
The probability that both will occur or the joint probability
P(AB) = P(A) P(B)
Total Probability Rule
P(A) = P(AS1) + P(AS2) + … + P(ASn)
Expected value
The probability-weighted average of the possible outcome of the random variable
E(X) = P(x1)X1 + P(x2)X2 + … + P(xn)Xn
Variance of a random variable
E [(x - E(x)) ^2]
Total Probability Rule for Expected Value
E(X) = E(X|s1)P(s1) + E(X|s2)P(s2) + … + E(X|Sn)P(sn)
Bayes’ Formula
P(Event | information) = P(information | event) / P(information) x P(event)
