Stats Ch. 6
Order by
28 terms
Terms | Definitions |
|---|---|
 chance behavior is unpredictable in the _______ run but has a regular and predictable pattern in the ______ run | short, long |
| random | individual outcomes are uncertain but there is nonetheless a regular distribution of outcomes in a large number of repetitions |
| probability | long-term relative frequency or the proportion of times the outcome would occur in a very long series of repetitions |
| independent | the outcome of one trial must not influence the outcome of any other |
| sample space S | the set of all possible outcomes in a random phenomenon |
| event | any outcome or a set of outcomes of a random phenomenon |
| probability model | a mathematical description of a random phenomenon consisting of two parts: a sample space S and a way of assigning probabilities to events |
| Multiplication Principal | If you can do one task in a number of ways and a second task in b number of ways, then both tasks can be done in a x b number of ways |
| with replacement | replacing the object after drawn to create an equal draw for the next round |
| without replacement | not replacing the object after drawn, creates a new probability for the next event |
| Any probability is a number between ______ | 0 and 1 |
| All possible outcomes together must have probability __________ | 1 |
| The probability that an event does not occur is 1 minus the probability that the event ______. | does occur |
| If two events have no outcomes in common, the probability that one or the other occurs is the sum of their __________________. | individual probabilities |
| probability rule one | The probability P(A) of any event A satisfies 0 ≤ P(A) ≤ 1. |
| probability rule two | If S is the sample space in a probability model, then P(S) = 1. |
| probability rule three | The complement of any event A is the event that A does not occur, written as Ac. The complement rule states that P(Ac) = 1 - P(A) |
| probability rule four | Two events A and B are disjoint (also called mutually exclusive) if they have no outcomes in common and so can never occur simultaneously. If A and B are disjoint, P(A or B) = P(A) + P(B) This is the addition rule for disjoint events. |
| {A ∪ B} | {A or B} |
| multiplication rule (independent events) rule 5 | Two events A and B are independent if knowing that one occurs does not change the probability that the other occurs. If A and B are independent, P(A and B) = P(A)P(B) This is the multiplication rule for independent events. |
| Rules of Probability | Rule1. 0≤P(A)≤1for any event A. Rule 2. P(S) = 1. Rule 3. Complement rule: For any event A,P(Ac) = 1 - P(A) Rule 4. Addition rule: If A and B are disjoint events, thenP(A or B) = P(A) + P(B) Rule 5. Multiplication rule: If A and B are independent events, then P(A and B) = P(A)P(B) |
| addition rule (disjoint) | P(one or more of A, B, C) = P(A) + P(B) + P(C) |
| addition rule (unions of two events) | For any two events A and B, P(A or B) = P(A) + P(B) - P(A and B) Equivalently,P(A ∪ B) = P(A) + P(B) - P(A ∩ B) |
| conditional probability | P(A | B) it gives the probability of one event under the condition that we know another event |
| general multiplication rule | The probability that both of two events A and B happen together can be found by P(A and B) = P(A)P(B | A) Here P(B | A) is the conditional probability that B occurs given the information that A occurs. |
| conditional probability | When P(A) > 0, the conditional probability of B given A is P(B|A) = P(AandB) P(A) |
| tree diagrams and the multiplication rule | the probability of reaching the end of any complete branch is the product of the probabilities written on its segments |
| independent events | P(B | A) = P(B) |
First Time Here?
Welcome to Quizlet, a fun, free place to study. Try these flashcards, find others to study, or make your own.