Algebra 2Mr. Gallo

11-2:Probability

Terms to KnowTerms to KnowProbability – is the ratio of the number of

_______________________ to the ___________ number of possible outcomes.

Probability = number of favorable outcomes

total number of possible outcomes

favorable outcomes total

RulesRulesProbability is expressed as a ______________,

____________, or _____________ with a value greater than or equal to _______________ and less than or equal to ___________.

(0 P 1)If P(A) = 0, then this represents an

___________________.If P(A) = 1, then this represents a

____________________.

fraction

decimal percent

zero

one

certain event

impossible event

Experimental ProbabilityExperimental ProbabilityExperimental probability – A calculation of the

probability of an event based on _______________________,____________________ or looking at the history of an event.

performing an experiment

conducting a survey

You observe 119 animals at a zoo, 19 of them have wings. What is the experimental probability that an animal at this zoo has wings?

19.16

119P W

Example 1:Example 1:The first exam grades of students in a

biology class are shown in the bar graph. Find the probability that a randomly chosen student in this biology class received a B or better. Total= 1 9 11 5 26

1 9 11 5

16

26

8

13

11 5

26

61.5%

or P B Better

SimulationsCan be used in place of expensive studies.

Used by John von Neuman and Stanislaw Ulam for behavior of neutrons during atomic bomb development.

Uses random numbers, die, coins, etc. to simulate situations and generate experimental probabilities.

Example 2:Example 2:On a multiple choice test, each item has three choices, but only one choice is correct. How can you simulate guessing the answers? What is the probability that you will pass the test by guessing at least five of ten answers correctly? 1.Use integers 1, 2, 3 to represent the three

answer choices.2.Assign 1 to represent the correct answer and 1

& 3 to represent the incorrect answers.3.Use RANDINT( Lowest integer, Highest Integer,

Number of outcomes). In the calculator type: randint(1,3,10) to represent the answers for the 10 questions.

4.Repeat the simulation at least 20 times, keeping track of results.

5.Use results to calculate experimental probability. Should be approximately 21.3%.

Homework: p. 685 #8-12, 42-45

Theoretical Probabilityis the number of outcomes divided by

the total number of outcomes and is often referred to as the ___________________ of an event.

probability

Example 3Example 3A standard die is rolled. Find each of the following:

a. The probability of rolling a 5.

b. The probability of rolling an even number.

c. The probability of rolling a number less than 3.

d. The probability of rolling a number greater than 7.

e. The probability of rolling a number less than 7.

1

6

3

6

1

2

2

6

1

3

0

60

6

61

Example 4Example 4A card is randomly selected from a deck of

cards. What is the probability of selecting a queen or a jack?

4 Queens in a deck 4 Jack in a deck

52 cards in a standard deck.

8

52

2

13

4 4

52

15.3%

number of favorable outcomes

total number of possible outcomes

Geometric probabilityGeometric probabilityGeometric probability – A type of

probability found by calculating a ___________________,____________, or ___________________.

ratio of two lengths

areas volumes

Example 5:Example 5:You throw a ball into a square basket.

What is the probability that it lands inside the circle? Assume that the ball is equally likely to hit any point inside the basket.

4279

45

Area of Circle

Area of Rectangle

.

L=9

W=5

r=2

Homework: p. 685 #13-21 odd, 24-26, 29-32