Transcript Probability

11-2:Probability
Algebra 2
Mr. Gallo
Terms to Know
 Probability – is the ratio of the number of
_______________________
to the ___________
total
favorable outcomes
number of possible outcomes.
 Probability =
number of favorable outcomes
total number of possible outcomes
Rules
fraction
 Probability is expressed as a ______________,
____________,
or _____________
with a value
decimal
percent
greater than or equal to _______________
and less
zero
than or equal to ___________.
one
(0  P  1)
 If P(A) = 0, then this represents an
impossible event
___________________.
 If P(A) = 1, then this represents a
____________________.
certain event
Experimental Probability
 Experimental probability – A calculation of the probability
of an event based on _______________________,
performing an experiment
____________________
conducting a survey or looking at the history of an
event.
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
P W  
 .16
119
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
11

5
P  B or Better  
26
16

26
8

 61.5%
13
1
9
11
5
Simulations
 Can 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:
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 Probability
 is the number of outcomes divided by the total number
of outcomes and is often referred to as the
___________________
of an event.
probability
Example 3
A standard die is rolled. Find each of the following:
a. The probability of rolling a 5. 1
6
b. The probability of rolling an even number. 3  1
6
c. The probability of rolling a number less than 3.
2
2
1

6
3
d. The probability of rolling a number greater than 7.
e. The probability of rolling a number less than 7.
0
0
6
6
1
6
Example 4
 A 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.
number of favorable outcomes
total number of possible outcomes
44
52
8

52
2

13
 15.3%
Geometric probability
 Geometric probability – A type of probability
found by calculating a ___________________,
ratio of two lengths
____________,
or ___________________.
areas
volumes
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.
Area of Circle
4

 .279
Area of Rectangle 45
r=2
W=5
L=9
Homework: p. 685 #13-21 odd, 24-26, 29-32