Statistics Chapter 5

Ace your homework & exams now with Quizwiz!

How to remember whether unions or intersection have more.

"Or has more ... than And" Also ∪ is like a cup which holds more than ∩

What is the sample space (S)?

The sample space S of a chance process is the set of all possible outcomes.

Mutually Exclusive

- A and B together is impossible: P(A and B) = 0 - A or B is the sum of A and B: P(A or B) = P(A) + P(B) (Addition rule for mutually exclusive events)

Not Mutually Exclusive

- A or B is the sum of A and B minus A and B: P(A or B) = P(A) + P(B) − P(A and B) (General Addition Rule for Two Events)

What are the rules of probability models?

- The probability of any event is a number between 0 and 1. - All possible outcomes together must have probabilities whose sum is 1. - If all outcomes in the sample space are equally likely, the probability that event A occurs can be found using the formula: P(A) = number of outcomes corresponding to event A/total numbers of outcomes in sample space - If two events have no outcomes in common, the probability that one or the other occurs is the sum of their individual probabilities.

What is a probability model?

A probability model is a description of some chance process that consists of two parts: a sample space S and a probability for each outcome.

What is an event?

An event is any collection of outcomes from some chance process. That is, an event is a subset of the sample space. Events are usually designated by capital letters, like A, B, C, and so on.

How to remember the union and intersection symbols.

Hint: To keep the symbols straight, remember ∪ for union and ∩ for intersection.

Multiplication rule for independent events

If A and B are independent events, then the probability that A and B both occur is P(A ∩ B) = P(A) • P(B).

Complement rule

P(AC) = 1 - P(A)

Conditional probability formula

P(B|A) = P(A ∩ B) / P(A).

General multiplication rule

The probability that events A and B both occur can be found using the general multiplication rule P(A ∩ B) = P(A) • P(B | A) where P(B|A) is the conditional probability that event B occurs given that event A has already occurred.

What is conditional probability?

The probability that one event happens given that another event is already known to have happened is called a conditional probability. Suppose we know that event A has happened. Then the probability that event B happens given that event A has happened is denoted by P(B | A).

What does it mean to say that two events are independent?

Two events A and B are independent if the occurrence of one event has no effect on the chance that the other event will happen. In other words, events A and B are independent if P(A | B) = P(A) and P(B | A) = P(B).

When are two events mutually exclusive (disjoint)?

Two events are mutually exclusive (disjoint) if they have no outcomes in common and so can never occur together. - Turning left and turning right are Mutually Exclusive (you can't do both at the same time) - Tossing a coin: Heads and Tails are Mutually Exclusive - Cards: Kings and Aces are Mutually Exclusive


Related study sets

Microeconomics Final Exam Written Portion

View Set

1.2 Indicators to type of attack

View Set

Foreshadowing in "The Monkey's Paw"

View Set

Chapter 10-The Wechsler Intelligence Scales: WAIS-IV, WISC-V, and WPPSI-IV (Exam 2)

View Set

Unit 3, WE ARE FAMILY: Las familias de los verbos

View Set

Older Adults Chapter 14 NRS 101 EXAM 4

View Set

Aice US history Western Expansion and the Civil War

View Set

BIOL 2404 - CH 15 - Digestive System

View Set