Theoretical Probability
Name:
HSPA Prep- Algebra II CP
Date:
Mrs. Sweet
Probability
Note Card Experiment:
What outcomes are possible?
Record your results after 20 attempts:
Combine your results with class:
When you gather data from observations you can calculate an
probability.
Experimental Probability:
P(event) = number of times the event occurs
number of trials
The Probability of an impossible event is
The Probability of a certain event is
Examples:
Of the 60 vehicles in the teacher’s lot today, 15 are pickup trucks. What is the experimental probability that a
vehicle in the lot is a pickup truck?
You observe 119 animals at a zoo, 19 of them have wings. What is the experimental probability that an animal
at the zoo will have wings?
Simulations: a
of an event.
On a multiple choice test each item has 4 choices but only one item is correct. What is the probability that you
will pass the test by guessing at least 6 out of 10 answers correctly?
Simulation on a Graphing Calculator: Go to: MATH
PRB
randInt(
Enter randInt( 1, 4, 10) This will randomly generate the numbers 1 through 4, 10 times.
Let a 1 represent a “correct” guess.
Record the number of “correct” guesses 19 more times.
How many tests had 6 or more “correct” guesses?
P(passing) =
number of passing test
number of tests taken
=
ENTER
The set of all possible outcomes to an experiment or activity is called a
space.
When each out come in a sample space has the same chance of occurring the outcomes are
outcomes.
Theoretical Probability:
If a sample space has n equally likely outcomes and an event A occurs in m of these outcomes, then the
m
theoretical probability of event A is:
P(A) =
n
Examples: What is the theoretical probability of each event?
1) getting a 5 on one roll of a standard number cube?
2) getting a sum of 5 on one roll of two standard number cubes?
4) getting an odd number on one roll of two standard number cubes?
Combinatorics: using the
count
Probability.
Principle, and ways to
to find Theoretical
and
What is the theoretical provability of being dealt exactly two 7’s in a 5 card hand from a standard 52 card deck?
A standard deck of cards has
ace, jack, queen and king.
suits. Each suit has cards numbered
through
The number of combinations of two 7;s from four 7’s is
The number of combinations of 3 non-sevens from the remaining cards is
The number of 5 card hands with two 7’s is
The number of 5 card hands is
P(hand with two 7’s) =
=
Example: What is the theoretical probability of being dealt exactly three 8’s in a 5-card hand from a
standard 52-card deck?
and an
Geometric Probability:
Using
to find theoretical probability.
A batter’s strike zone depends on the height and
stance of the batter. What is the geometric
probability that a baseball thrown at random withing
the batter’s strike zone, as pictured left, will be a highinside strike?
Example: A carnival game consists of throwing darts at a circular board as shown. What is the geometric
probability that a dart thrown at random will hit the shaded circle?