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)

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

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.

Conditional Probability

In probability theory, conditional probability is a measure of the probability of an event given that another event has occurred.

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.

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).

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.

law of large numbers

if we do something many many times, the proportion of desired outcomes will approach its probability

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

prob in the long term

predictable

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

if 3 probabilities = 1, then

they will always occur

probability in the short term

unpredictable

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).

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.