Statistic Chapter 17 PowerPoint Quizlet

P(Event) equation?

(Number of successful outcomes)/ (Total number of outcomes)

Outcomes of random phenomena settle down in the ______-run to something ____ and _____.

-long-run, consistent, predictable -We would expect each side to land 1/6 of the time in the long run

The relative frequencies are ______ probabilities; they _______ probabilities

-not -approximate

Classical Probability ( Equally likely ______ )

-outcomes

Random Phenomenon --> -Situation in which we know all of the ______ outcomes that can occur, but not the _______outcome that will occur

-possible -particular

-A measure of the likelihood of occurrence of an event is called ________ ___ ≤ probability ≤ _____

-probability - 0 ≤ probability ≤ 1

Rules A --> _____ ≤ P(event) ≤ _____

0, 1

Rule B ---> All possible outcomes together = _____

1

Thus, P(Event occurs)+P(Event does not occur)=____

1

For a fair die, what is the probability that the die lands either on 1 or 2 or 3 or 4 or 5 or 6? Answer = ______ It's a ____ event that the die will land on ____ of those numbers

1 -certain 1

....

-No, because the various outcomes are not equally likely

....

-estimate probabilities, theoretical probabilities, repeat

We would expect each side to land _____ of the time in the long run

1/6

-Each iteration of an experiment is called a ______

Trial

Total number of outcomes --> -the number of outcomes in the ______ space

sample

For example: There are 6 beads in a bag, 3 are RED, 2 are GREEN, and 1 is BLACK. What is the probability of picking a GREEN bead? (Find the Event, Sample Space, Equally likely that____

-P(Picking a GREEN Bead) = (# of Green Beads in the Bag)/(Total # of Beads in the Bag) -P(Picking a Green Bead) = (2/6) = (1/3) -Event- picking a green bead -Sample Space: R, R, R, G, G, B -Equally likely that any of the 6 beads can be selected

Examples of an Experiment

-Rolling a die, Sample space: (1,2,3,4,5,6)

Equal likely outcomes --> _____ possible outcomes of an experiment have the chance of occurring

-all

P(Event A does not occur)=

- 1 - P(Event A occurs)

Law of Large Numbers ---> -If we repeat a random phenomenon, the relative frequencies gets ____ to the theoretical probabilities the more times we repeat the experiment

-closer

P(Rolling a 2 or a 4 on one toss of a fair die) = ______

- (2/6)= (1/3)

P(NOT rolling a 2 or a 4) =_______, which is equivalent to _______

- 1- (1/3) = (2/3)= (4/6), which is equivalent to P(Rolling a 1 or 3 or 5 or 6)

Empirical Approach (______ Frequency) 1) Conduct many _____ of an experiment to generate data 2) Obtain the _____ frequency of an event of interest and use that to estimate (P(Event)\ 3) If an experiment is repeated n times and an Event A is observed f times, then, according to the empirical/relative frequency approach: ______

-(Relative Frequency) -trials -relative -f/n

How many Outcomes are Possible if we Roll 2 Dice? (Slide 7)

-6 ways for the first die * 6 ways for the second die= 36 possible outcomes in the sample space

These types of events are called ____ events

-Complementary

Examples of Random Phenomenon

-Ex: Which side of a six-sided die will land face up when we roll the die? -We cannot predict with certain with certainty the side that will land face up on a particular roll of the die

Could we use the Classical Approach or the Relative Frequency approach to calculate the following probability?

-No

....

-P(I roll a 5 with a fair die)? - Given info -P( I roll a 5 with a fair die/ I rolled a five on last throw of the same die)? -P(A couple's sixth child is a girl/their first five children are boys)?

Experiment ----> -Any process that can be _______ repeated and has a ______-defined set of possible outcomes

-infinitely -well

A set of outcomes of an experiment is called an _______

Event

We have a die that is weighted--> - P(the die landing on each of the 6 sides) is ______ equally likely- but we don't know how the die is weighted Could we use the classical approach to calculate P(we toss the die & it lands on a 4)?

NOT No because the chances are not equally likely

....

Probability(Event A) ≅ (Frequency of Event A/ Total number of trials) =( f/n )

You roll 2 fair 6-sided dice once. What is the probability of getting the sum of 7?

Probability= (6/36)=(1/6)

Well-defined set of possible outcomes is called __________

Sample Space

Number of successful outcomes---> the number of ways that can event _____ occur

can