Transcript Probability

You can do this! 
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Event
Outcome
Probability
Sample Space
Compound Events
Independent Event
Dependent Event
Tree Diagram
Organized List
Counting Principle
Experimental Probability
Theoretical Probability
Likelihood
Impossible Event
It’ll NEVER
happen!!!
It is not very
likely it’ll
happen.
Certain Event
It might
happen
There is a
strong
chance it’ll
happen
It’ll
definitely
happen!!!
Possible Events:
1. The likelihood of having homework tonight.
2. The likelihood of having a tornado warning today.
3. The likelihood of having a two hour delay tomorrow.
Can you think of one?
It’ll NEVER
happen!!!
It is not very
likely it’ll
happen.
It might
happen
There is a
strong
chance it’ll
happen
It’ll
definitely
happen!!!
 A spinner has 4 equal sections colored
blue, yellow, green, and red. What are the
chances of landing on blue after spinning
the spinner?
 Experiment: spinning the spinner.
 Outcome: possibilities (yellow, blue,
green or red).
 Event: Landing on blue.
 Probability: Favorable event / possible
outcomes.
What is probability?
The likelihood of an event occurring.
Probability = _______________________
What are the odds of flipping a coin and
landing on heads?
When all possible events or outcomes are equally likely to occur, the
theoretical probability can be found without collecting data from an
experiment.
P (event) =
Number of favorable outcomes
Total number of possible outcomes
Data is collected through observations or experiments.
Each result from the experiment is called an event.
The probability of an event is equal to the
number of times an event occurs divided by
the total number of experiments.
P (event) =
Number of times an event occurs
Total number of experiments
Number of times an event occurs
P (event) =
Total number of experiments
Event = scoring a basket
Number of baskets scored
Number of shots taken
 The probability of rolling a 2 on a 6 sided number
cube.
Theoretical
 After rolling a die 50 times, the number of times you
rolled a 2.
Experimental
 The probability of drawing an ace based off of
choosing 15 cards from a deck at random.
Experimental
 The probability of choosing an ace from a deck of
cards.
Theoretical
 A bag contains 3 white marbles, 5 blue marbles and 7
red marbles. What is the probability of drawing a blue
marble at random?
 How many marbles are blue?
 How many marbles all together?
 What is the probability as a fraction, decimal and
percent?
 If you shuffle a deck of cards and draw a card at
random, what is the probability that the card you
chose would be a king?
Questions to ask yourself…
 How many cards are in a deck?
 How many kings are in a deck?
 What is the probability?
 If you rolled a six sided die, what is the probability that
you would roll and even number?
A. 1/6
C. 6/6
B. 2/6
D. 1/2
 A bag contains 6 black marbles, 9 red marbles, 12
white marbles, and 3 green marbles. What is the
probability of drawing a red marble?
A. 3/10
C. 3/5
B. 6/30
D. 12/30
**OR = ADD**
 If rolling a 6 sided die, what is the probability of
rolling a 2 or a 6?
In this case you could have a successful outcome if you
roll a 2 or a 6.
Number of favorable outcomes
Number of total outcomes
=
 If you were to spin this spinner, what
would the probability be of landing
on bankrupt or lose turn?
P (bankrupt or lose turn)
 A bag contains 2 black marbles, 9 red marbles, 12
white marbles, and 5 green marbles. What is the
probability of drawing a black or a green marble?
 What is the probability of picking a card out of a
standard deck and drawing a jack or 4?
A.
C.
B.
D.
 What is the probability of picking a card out of a
standard deck and drawing a queen, king, or jack?
A.
C.
B.
D.
Probability Worksheet
PLEASE SHOW YOUR WORK!!
No homework passes for this assignment!
(Sorry)
What is the probability
of drawing a jack out of
a standard deck of
cards?
What is the probability
of rolling a 4 or 5 on a
six sided number cube?
*If I draw cards from a
deck 50 times to
determine the probability What is the probability of
of pulling a face card, am drawing a red ace from a
I using theoretical or
standard deck of cards?
experimental probability?
 Shows all possible outcomes in an
organized drawing.
 First write a list down the paper of the first item, in this
case 1 to 5
1
2
3
4
5
 Now determine how many options there are for the
second item
There are 3 options:
Red
White
Blue
 Draw “branches” off of each number. One for
each second item, in this case 3.
1
2
3
4
5
 At the end of each branch, write one of the
three options from the 2nd items given.
1
R
W
B
2
R
W
B
3
R
W
B
4
R
W
B
5
R
W
B

There are five different times the color red could be chosen
from all 15 options
 The chance of having the color red is 5/15 or reduced is
1/3
 How many combinations of sandwiches can you make
with the following options?
Types of Bread
*Wheat
*Italian
*Rye
Fillings
*Cheese
*Ham
*Turkey
*Salami

Give the total number of outcomes of
choosing a hamburger, hot dog, or chicken
and potato salad, coleslaw, or beans. Use a
tree diagram.
 Another way to determine how many possibilities. Create a
list of all options.
 How many possible outcomes are there with a red,
blue or green sock and a black or white shirt?
List: Red & Black, Red & White, Blue & Black, Blue
& White, Green & Black, Green & White.
How many outcomes?
Shirts
*Blue
*Red
*Green
*Yellow
Pants
*Black
*Brown
 YES!
 Multiply the number of possibilities in the first set by
the number of possibilities in the second set.
 Example:
2 colors (red, blue), numbers 1 -5 numbers: 2 × 5 = 10
List: red 1, red 2, red 3, red 4, red 5, blue 1, blue 2, blue 3,
blue 4, blue 5
 How many combinations can you have with 3 colors
and 10 numbers?
A. 13
C. 30
B. 15
D. 7
 How many combinations are in a sample space with
rolling 2 dice and tossing a coin?
A. 72
C. 12
B. 80
D. 36
 What is it?
 An event that consists of two or more simple events.
Steps:
*Determine all outcomes for each event.
*Multiply number of outcomes.
*Find all favorable events.
 Two events, A and B, are independent if the fact that
A occurs does not affect the probability of B occurring.
 Landing on heads after tossing a coin AND rolling a 5 on
a single 6-sided die.
 Choosing a marble from a jar AND landing on heads
after tossing a coin.
 Choosing a 3 from a deck of cards, replacing it, AND
then choosing an ace as the second card.
 Rolling a 4 on a single 6-sided die, AND then rolling a 1
on a second roll of the die.
 Multiplication Rule : When two events, A and B, are
independent, the probability of both occurring
is: P(A and B) = P(A) · P(B)
 Each spinner is divided into equal sections. The two
spinners are spun together . What is the probability of
landing on blue and an even number?
 A coin is tossed and a single 6-sided die is rolled. Find
the probability of landing on the head side of the coin
and rolling a 3 on the die.
 A jar contains 3 red, 5 green, 2 blue and 6 yellow
marbles. A marble is chosen at random from the jar.
After replacing it, a second marble is chosen. What is
the probability of choosing a green and then a yellow
marble?
A.
C.
B.
D.
 What is the probability of rolling an even number on a
die and tossing a coin and landing on tails?
A. 1/2
C. 1/4
B. 1/8
D. 2/3
 Two events are dependent if the outcome or occurrence of
the first affects the outcome or occurrence of the second so
that the probability is changed.
Multiplication Rule 2: When two events, A and B, are
dependent, the probability of both occurring is: P(A and
B) = P(A) · P(B|A)
 Experiment 1: A card is chosen at random from a standard
deck of 52 playing cards. Without replacing it, a second card
is chosen. What is the probability that the first card chosen is
a queen and the second card chosen is a jack?
 Mr. R needs two students to help him with a science
demonstration for his class of 18 girls and 12 boys. He
randomly chooses one student who comes to the front of
the room. He then chooses a second student from those
still seated. What is the probability that both students
chosen are girls?
 Three cards are chosen at random from a deck of 52
cards without replacement. What is the probability of
choosing 3 aces?
A.
C.
B.
D.
 In Mr. M’s room, students are being assigned to group
projects by drawing colored chips from a bag. Once
selected, the marbles will not be returned to the bag.
There are 4 blue chips, 5 green chips, 5 red, 4 yellow chips,
4 black chips and 4 white chips. What is the probability
the first and second students will draw yellow chips?
A. 1/3
C. 2/650
B. 6/325
D. 2/3
What is the probability
What is the probability of drawing a six of clubs
of rolling a 2 or 3 on a six from a standards deck of
sided number cube?
playing cards?
*What is the probability
of flipping a coin and
landing on heads and
rolling a die and landing
on 2 or 4?
Two cards are drawn from
a standard deck of playing
cards without replacing it.
What is the probability
that the first card is an ace
and the second is a 4?