SECTION 4.2

BASIC CONCEPTS OF PROBABILITY

PROBABILITY

● The chance a situation will happen / occur

● Answers will be written in– Fraction form

– Decimal form

– Percents are usual not used in Statistics, they are reserved for algebra :)

QUESTION

● What is the probability of picking a red car?●

KEY TERMS

● Event– any collection of results or outcomes of a

procedure

● Simple Event – an outcome or event that cannot be further

broken down into simpler components

● Sample Space

– consists of all possible events, or outcomes

NOTATIONS

P - probability

A - specific event

a - amount in the specific event

T - sample space

t - amount in the sample space

● P(A) - probability of event A occurring

DEFINITION

P (A)= Number for event ANumber for Sample Space=

at

EXAMPLE

Given the set find the probability of choosing a red ball.

EXAMPLE

Given the group of cars, find probability that a yellow car will win the race.

EXAMPLE

Given the group of cars, find probability that a pink car will win the race.

Important Principles

● The probability of event A occurring

0 ≤ P(A) ≤ 1● The probability if event A is impossible to occur

P(A) = 0● The probability if event A is certain to occur

P(A) = 1● The probability event A's complement will occur

P(A') = P(AC) = P(A) = 1 - P(A)

EXAMPLE

● Find the probability of not choosing a red ball.

TABLE

Positive Test Results

Negative Test Results

Subject uses Drugs

44 6

Subject is not a Drug User

90 860

EXAMPLE

● Given the table find the probability of selecting someone who does not use drugs.

EXAMPLE

● Is this result close to the probability of 0.866 for a negative test result

UNLIKELY / LIKELY

● An event is unlikely if its probability is very small, such as 0.05 or less

● An event is likely if its probability is very high, such as 0.95 or higher

UNUSUAL

● An event is unusual if the z-score is less than -2 or greater than 2.

EXAMPLE

● In a survey, 169 respondents say that they never use a credit card, 1227 say that they use it sometimes, and 2834 say that they use it frequently.

● What is the probability that a randomly selected person uses a credit card frequently?

● Is it unlikely for someone to use a credit card frequently?