Module 8.1: Conditional and Joint Probabilities Flashcards
What is a random variable, outcome, event, mutually exclusive event, and exhaustive events? Use dice as an example.
Consider rolling a 6-sided die. The number that comes up is a random variable. If you roll a 4, that is an outcome. Rolling a 4 is an event, and rolling an even number is an event. Rolling a 4 and rolling a 6 are mutually exclusive events. Rolling an even number and rolling an odd number is a set of mutually exclusive and exhaustive events.
What are the two defining properties of probability?
1) The probability of an occurence of any event is between 1 and 0
2) If a set of events is mutually exclusive and exhaustive, the probabilities of those events sum to 1.
What is an empirical, a priori, and subjective probability?
Empirical - established by analyzing past data
a priori - determined using a formal reasoning and inspection process.
Subjective - least formal method, use of personal judgemnet.
What are the odds an event will occur if the probability of occurance is one-eighth?
The odds would be (1/8)/(7/8) or 1/7.
If we are given the odds of an event, we can calculate the probability of occurance the opposite way.
If odds were 1/8, the probability of occurance would be 1/9.
What is an unconditional probability vs. a conditional probabiliy?
Unconditional - probability of an event regardless of the occurence of other events.
Conditional - One occurance affects the probability of another.
Probability of A given B is written P ( A | B)
What is the multiplication rule of probability? What is the formula?
Used to determine the joint probability of two events.
P(AB) = P(A|B) x P(B)
What is the additional rule of probability? What is the formula?
Used to determine the probability of at least one of two events occurring.
P (A or B) = P(A) + P(B) - P(AB)
What is the total probability rule? What is the formula?
Used to determine the unconditional probability of an event, given conditional probabilities.
P(A) = P(A | B1)P(B1) + P(A | B2)P(B2) + … + P(A | BN)P(BN)
B1, B2, BN are mutually exclusive events and exhaustive.
