5 minute check, 26 sep › cms › lib02 › sc01001931...title: 5 minute check, 26 sep author: rob...
TRANSCRIPT
-
Geometry HSAP Review, Mar 26
Probability
Book Sections: N/A
Essential Questions: What is simple probability, what are its components, where do I find it and how do I compute it? What is
multiple event probability?
Standards: N/A
-
Part 1
• Simple probability – One thing happening.
-
Notation
• The probability of an event will be
abbreviated as follows:
P(event) =
-
The Mathematical Definition of Probability
P(event) =
In words: The probability of an event is the ratio of favorable outcomes to the number of possible outcomes. That number will always be between 0 and 1.
Number of favorable outcomes
Total number of outcomes
-
What Are the Components of the Ratio
• Favorable outcomes – The number of ways within the sample space
that what you want to occur CAN occur
• Total number of outcomes – everything that can happen in the
sample space
The total number of outcomes is also known as all possible
outcomes
-
Some Simple Examples Total Number of Outcomes
If you roll a single fair die, there are 6 possible outcomes, which are
1, 2, 3, 4, 5, 6
Drawing a single card from a deck. There are 52 possible outcomes.
Flipping a coin has two possible outcomes, a head or a tail.
-
Some Simple Examples Favorable Outcomes
Betting on the number 5 on a roll of a die.
Selecting an even number on a roll of a die.
Selecting a red card from a deck of cards.
Selecting a queen from a deck of cards.
Selecting the 5 of diamonds from a deck of cards.
Calling heads on a coin flip.
-
Computing Probabilities
The number 5 on a roll of a die.
Selecting an even number on a roll of a die.
Selecting a red card from a deck of cards.
Selecting a queen from a deck of cards.
Selecting the 5 of diamonds from a deck of cards.
Calling heads on a coin flip.
-
More Examples
-
Expressing Probability
• Probability can be expressed as:
A fraction (in simplest form)
A decimal
A percent (%)
• Probability ranges between 0 and 1
Probability of 0 means the event is impossible
Probability of 1 means the event is a sure thing
-
Examples A bag contains 4 red, 3 blue, 2 green, and 1 yellow
marble. Compute the following probabilities based on
selecting a single marble from the bag:
-
Part 2
• Multiple event probability – More than one
thing happening.
-
The Probability of a Single Event
P(event) =
Number of favorable outcomes
Number of possible outcomes
-
Multiple Event Methodology
• Anytime we do multiple events, and they
involve the word and – meaning both, we
are multiplying probabilities.
-
Multiple Events
• Multiple Events – More than one random
event occurring simultaneously or in
succession.
• Multiple events are either independent or
dependent events
-
How Can I Tell the Difference
• Drawing or selecting anything from a pool
of objects and then selecting another
without replacing the first is an indication of
dependency
• A situation where there is a cause – effect
relationship
• Anything else, including selection with
replacement or from different sources, are
independent events
-
Independent or Dependent?
1. Tossing a coin and spinning a spinner
2. Drawing two cards from a single deck
3. Drawing two cards from separate decks
4. Selecting two marbles from a bag of marbles
5. Being a lifeguard and getting a suntan
6. Betting on different horses to win, place, and
show at the track
7. Rolling two dice
8. Parking in a no parking zone and getting a
parking ticket
I
D
I
D
D
D
I
D
-
Multiple Event Probabilities 1
• Multiple events are called event A and event B
A and B are independent
• P(A and B) = P(A) · P(B), P(A) and P(B) are simple
probabilities
-
An Example
P(7and 4)
P(even and odd)
P(yellow and red)
-
Multiple Event Probabilities 2
• Multiple events are called event A and event B
A and B are dependent
• P(A and B) = P(A) · P(B | A), where P(A) is a simple
probability and P(B | A) is a probability computed for B
given that A has already happened
-
Example • Bag A contains 10 marbles of the following colors:
4 green, 3 blue, 2 red, and 1 purple.
P(blue and red)
P(red and green)
P(green and gray)
P(green and green)
-
Adjusting a Sample Space
To compute P(B following A) – Two Steps to
adjusting a sample space:
1. There are now one less items in the space
2. The item ‘selected’ is not there, debit that
mini pool.
-
Multiple Event Probabilities
• Multiple events are called event A and event B
A and B are dependent
• P(A and B) = P(A) · P(B | A), where P(A) is a simple
probability and P(B | A) is a probability computed for B
given that A has already happened
A and B are independent
• P(A and B) = P(A) · P(B), P(A) and P(B) are simple
probabilities
-
Multiple - Multiple Events
• What if its more than two events?
• Assess the situation, compute probabilities,
keep multiplying
If dependent, think P(C | A and B)
-
Example
A person owns a collection of 30 CDs, of which 5 are country
music. If two CDs are selected randomly, what is the
probability that both are country music?
-
Working With All Multiple
Events
1. Determine dependency (Indep or Dep)
2. Visualize or draw a picture of sample space
3. Compute probability of first event
4. Compute probability of second event
Adjust sample space if a dependent event
5. Multiply probabilities together
6. Simplify (if required)
-
Homework: None
Class work: Handout CW 3/26, all