Probability Models Section 6 2 Sample Space S

Probability Models Section 6. 2

Sample Space S • The set of all possible outcomes

Event • Any outcome or set of outcomes of a random phenomenon • A subset of the sample space

Probability Model • A mathematical description of a random phenomenon consisting of two parts 1. Sample space S 2. A way of assigning probabilities to events

Multiplication Principle • 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 ab number of ways

Types of Sampling • With replacement • Without replacement

Probability Rules 1. The probability P(A) of any event A is between 0 and 1 inclusive 2. If S is the sample space in a probability model, then P(S) = 1

3. The complement of any event A is the event that A does not occur, written Ac. The complement rule states that P(Ac) = 1 – P(A).

• 4. Two events A and B are disjoint (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.

Venn Diagram • Shows the sample space S as a rectangular area and events as areas within S

Probabilities in a Finite Sample Space • Assign a probability to each individual outcome, probabilities must be between 0 and 1 • Probability of any event is the sum of the probabilities of the outcomes making up the event

Equally Likely Outcomes • If a random phenomenon has k possible outcomes, all equally likely, then each individual outcome has probability 1/k

Rule 5 • Multiplication Rule for Independent Events • Two events A and B are independent if knowing that one occurs does not change the probability that the other occurs • P(A and B) = P(A)P(B)

NOTE: • Disjoint events are not independent.

Practice Problems • pg. 356 #6. 34 -6. 45