Probability Flashcards
What are the two fundamental ways we can determine probability?
- theoretical (aka classical)
2. emperical (aka observational)
When are classical methods of probability used?
games of chance
Why is theoretical method also called classical
because their values are determined by the game itself (the nature of the situation… 6 sided dice)
What is probability?
a way of quantifying uncertainty
What do empirical methods use to determine probability?
series of random experiments/trials to produce outcomes that cannot b predicted in advance
When a simulation is run or a random sample is used and the results recorded, is theoritical or empirical probability in play?
empirical
What is the relative frequency of probability
using empiracal probability (simulations, etc) to prove the theoretical probability
what is the formula for relative frequency?
number of times A occurred / total number of repetitions
What is the Law of Large Numbers?
the relative frequency of an event does approach the theoretical probability of that event as the number of repetitions increases
What is a sample space?
A list of all possible outcomes the random experiment can produce
What are the 11 basic probability rules?
- For any event A, 0 ≤ P(A) ≤ 1
- P(S) = 1
- Compliment rule: P(not A) = 1 - P(A)
or
P(A) = a - P(not A) - If A and B are disjoint events, then P(A or B) = P(A) + P(B)
- If A and B are independent, then P(A and B) = P(A) * P(B)
- General Addition Rule: For any 2 events A and B, P(A or B) = (PA) + P(B) - P(A and B)
or if disjoint:
P(A or B) = P(A) + P(B) - Multiplication Rule for Independent Events: P(A and B) = P(A) * P(B)
What does Probability rules 1: 1. For any event A, 0 ≤ P(A) ≤ 1 mean?
that the probability of any event can range between 0 and 1
What does Rule 2: P(S) = 1 mean?
the sum of all the probabilities of all possible outcomes is 1
What does Rule 3: P(not A) = 1 - P(A) mean?
probability that an event does not occur is 1 minus the probability that it does occur
What is disjoint or mutually exclusive?
when two events cannot occur at the same time
What does Rule 4: If A and B are disjoint events, then P(A or B) = P(A) + P(B) mean?
If the two events are disjoint, and you are looking for the probability of A or B occurring, then P(A) and P(B)
In probability, does “or” mean multiplication, division or addition?
addition
What does rule 5: P(A and B) = P(event A occurs and event B occurs) mean
means you find the the overlap of these two probabilities occurring at the same time
in probability, does “and” mean division, multiplication or addition?
multiplication
If two events are disjoint, what would be P(A and B)
0, because they cannot occur at the same time
Define independent events
if the fact that one event occurs and it does not affect the probability that the other event will occur
If two events are not disjoint, but are independent, will P(A and B) be greater than 0
yes, because they can still occur at the same time, they just have no affect on each other.
If two events are disjoint, can they be independent?
if two items cannot occur at the same time, then they can’t have a direct affect on each other.
What rule(s) can be used when finding “at least one of”
- compliment rule:
P(at least one of several events occur) = 1-P(none of the events occur)
How is conditional probability notated:
(A | B)
A = the probability we seek
B = the given
What is the formula for conditional probability?
P(B|A) = (A and B) / P(A)
always divide by the given event
How can you determine if two events are dependent on each other (4)
Compare:
1. P(A | B) and P(A)
- P(A | B) and P(A | not B)
- P(B | A) and
P(B | not A) - P(A and B) = P(A) * P(B)
What is the general multiplication rule for dependent events?
P(A and B) = P(A) * P(B|A)
