stats chap 5
general addition rule
P(A or B) = P(A) + P(B)
probability is
always a number between 0 and 1
complement
probability of an event not happening P(A^c)=1-P(A)
what is the difference between independent and mutually exclusive?
Mutually exclusive events cannot happen at the same time. For example: when tossing a coin, the result can either be heads or tails but cannot be both. Events are independent if the occurrence of one event does not influence (and is not influenced by) the occurrence of the other(s).
law of large numbers
if we do something many many times, the proportion of desired outcomes will approach its probability
if 3 probabilities = 1, then
they will always occur
probability in the short term
unpredictable
above 5%
shows something is not statistically significant
below or = to 5%
shows something is statistically significant= very unlikely to have occurred
the probability of any outcome of a random phenomenon is
the proportion of times the outcome occurs in a very long series of repetition
how do you know if two things are independent?
Events A and B are independent if the equation P(A∩B) = P(A) P(B) holds true. You can use the equation to check if events are independent; multiply the probabilities of the two events together to see if they equal the probability of them both happening together.
independent statistics definition
Independent Events. When two events are said to be independent of each other, what this means is that the probability that one event occurs in no way affects the probability of the other event occurring. An example of two independent events is as follows; say you rolled a die and flipped a coin. when knowing if an event has or has not occurred does not affect the prob of the second event.
prob in the long term
predictable
a die is loaded so that the number six comes up 3 times as often as any other number... wha is the probability of rolling a one or a 6?
12345666= 1/2
Conditional Probability
In probability theory, conditional probability is a measure of the probability of an event given that another event has occurred.
conditional probability equation
P(A|B) = P(A and B) / P(B)
mutually exclusive definition
Two events are mutually exclusive if they cannot occur at the same time. Another word that means mutually exclusive is disjoint. If two events are disjoint, then the probability of them both occurring at the same time is 0.
more about the general addition rule
Addition Rule 1: When two events, A and B, are mutually exclusive, the probability that A or B will occur is the sum of the probability of each event. Addition Rule 2: When two events, A and B, are non-mutually exclusive, there is some overlap between these events.
complementary
Complementary events are two outcomes of an event that are the only two possible outcomes. This is like flipping a coin and getting heads or tails. ... Rolling a die and getting a 1 or 2 are not complementary since there are other outcomes that may happen (3, 4, 5, or 6).
when looking at a probability table, the numbers must all equal
must add to 1 and all must be between 0 and 1- list showing all possible outcomes and their probabilities