Probabilities Flashcards
It is a process that generates data
Experiment
It is the set of all possible outcomes of a probability experiment
Sample space
It is an outcome in a sample space
Sample point
It is a subset of a sample space
Event
It is the set of all elements of a sample S that are not in event A given that the said event occurs with respect to S
Complement (A^’)
The event containing all the elements that are in events A or B or both
Union ( A U B )
An event containing common elements from events A and B
Intersection ( A ∩ B )
How can we say that events A and B are mutually exclusive?
If they have no intersection ( A ∩ B = ∅ )
It is a function that shows the chances of an event to occur
Probability
What are the 4 axioms of the probability of an event A from the sample space S of an experiment?
- The probability that an event A occurs is always nonnegative (0 ≤ P(A) ≤ 1)
- The probability of the sample space’s occurrence is always 1 (P(S) = 1)
- P(A) = 0 is called an improbable event
- if events E1, E2, … En, are all mutually exclusive events from S, then the summation of P(Ei) = 1
It is used when the sample points are measured the same / equally likely to occur
Classical probability
A coin is tossed 5 times. What is the probability that:
a. exactly 3 heads will occur?
b. at least 2 heads will occur?
In a poker hand consisting of 5 cards, find the probability of holding 2 aces and 3 jacks.
A die is loaded in such a way that an even number is twice as likely to occur as an odd number. If E is the event that a number less than 4 occurs on a single toss of the die, find P(E).
It summarizes the counts of elements that belong to two categories
It is often used to facilitate the calculation of probabilities involving two events
Contingency Table (Summary of Probabilities)
