# Stats Ch. 6

## 28 terms

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

0 and 1

1

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 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)

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

P(B | A) = P(B)

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