Probability

1
Probability
2

• Tree Diagram A diagram with branches that is
  used to list all possible outcomes.
• Example Meal choices Burger, hot dog, Pizza
  Drinks coke or sprite

3

• Sample space A list of all the possible
  outcomes.
• Example The sample space for rolling a dice is
• 1, 2, 3, 4, 5, 6.
• Counting Principle a way to find the number of
  possible outcomes of an event.
• Just multiply the number of ways each activity
  can occur.

4
Try the following

• Andy flips a coin and spins a spinner with 3
  equal sections marked A, B, C. a) Draw a tree
  diagram, b) What is the sample space (i.e. all
  possible outcomes)? How many outcomes are in the
  sample space?
• HA TA
• HB TB 6 outcomes
• HC TC

5

• For the lunch special at Nicks Deli, customers
  can create their own sandwich by selecting 1 type
  of bread and 1 type of meat from the selection
  below.
• c
• a) In the space below, list all the possible
  sandwich combinations using 1 type of bread and 1
  type of meat.
• WC RC
• WRb RRb
• b) If Nick decides to add whole wheat bread as
  another option, how many possible sandwich
  combinations will there be?
• 6 outcomes

6

• Helen is preparing candy bags for the children
  at a party. She has 2 flavors of lollipops, 4
  types of candy bars, and 6 flavors of chewy
  candies. If each bag contains one piece of each
  type of candy, what is the total number of
  possible candy combinations for the bags?
• A) 12 B) 15 C) 36 D) 48

7

• Peter has 6 sweatshirts, 4 pairs of jeans, and 3
  pairs of shoes. How many different outfits can
  Peter make using one sweatshirt, one pair of
  jeans, and one pair of shoes?
• A) 13 B) 36 C) 72 D) 144

8

• Erin wants to make a sandwich from the main
  ingredients shown in the table below.
• In the space below, list all the possible ways
  Erin can make a sandwich using one type of bread
  and one main ingredient.
• SP SH ST SE
• WP WH WT WE
• RP RH RT RE

9

• Probability is the likelihood that an event will
  occur.
• Probability of getting a tail when tossing a coin
• Experiment an activity involving chance, such as
  rolling a cube
• Tossing a coin is the experiment
• Trial Each repetition or observation of an
  experiment
• Each time you toss the coin is a trial

10

• Outcome A possible result of an event.
• Example Heads or tails are possible outcomes
  when tossing a coin
• Event A set of one or more outcomes
• Example Getting a heads when you toss the coin
  is the event
• Compliment of an Event The outcomes that are not
  the event
• Example Probability of rolling a 4 1/6. Not
  rolling a 4 5/6.

11

• Probability is always between 0 and 1.
• Probability 0 means that the event will NEVER
  happen.
• Example The probability that the Bills will win
  the Super Bowl this year.
• Probability 1 means the event will ALWAYS
  happen.
• Example The probability that Christmas will be
  on December 25th next year.

12


_______________
_______________
_______________
13

• Rolling a 0 on a number cube
• Impossible
• Rolling a number less than 3 on a number cube
• Unlikely
• Rolling an even number on a number cube
• Equally likely
• Rolling a number greater than 2 on a dice
• Likely
• Rolling a number less than 7 on a number cube
• Certain

14

• Experimental Probability is based on an
  experiment. The probability of what ACTUALLY did
  happened.

15
Try the following

• Example 1 During football practice, Sam made 12
  out of 15 field goals. What is the probability he
  will make the field goal on the next attempt?3
• 12/15
• Example 2 Ms. Sekuterskis student have taken
  out 85 books from the library. 35 of them were
  fiction. What is the probability that the next
  book checked out will be a fiction book?
• 35/38

16

• Example 3 Emma made 9 out of 15 foul shots
  during the first 3 quarters of her basketball
  game. What is the probability that the next time
  she takes a foul shot she will make it?
• 9/15
• Example 4 Christina scored an A on 7 out of 10
  tests. What is the probability she will score an
  A on her next test?
• 7/10

17

• Theoretical Probability the probability of what
  should happen. Its based on a rule
• of favorable outcomes
• of possible outcomes
• Example Rolling a dice and getting a 3

18

• Example 1 Andy has 10 marbles in a bag. 6 are
  white and 4 are blue. Find the probability as a
  fraction, decimal, and percent of each of the
  following
• a) P(blue marble)
• 4/10
• b) P(white marble)
• 6/10
• Example 2 If there are 12 boys and 13 girls in
  a class, what is the probability that a girl will
  be picked to write on the board?
• 13/25

19

• Example 3 There are 8 black chips in a bag of 30
  chips. What is the probability of picking a black
  chip from the bag?
• 8/30
• Example 4 There are 2 small, 5 medium, and 3
  large dogs in a yard. What is the probability
  that the first dog to come in the door is small?
• 2/10

20

• Example 5 What is the probability of getting a
  tail when flipping a coin?
• 1/2
• Example 6 What is the probability of rolling a 4
  on a die?
• 1/6

21

• Independent the outcome of one event DOESNT
  effect the probability of another event
• Example Find the probability of choosing a green
  marble at random from a bag containing 5 green
  and 10 white marbles and then flipping a coin and
  getting tails.
• 5/15 x ½ 5/30 1/6

22

• Replacement DOESNT effect the probability of
  another event
• Example A drawer contains 3 red paperclips, 4
  green paperclips, and 5 blue paperclips.  One
  paperclip is taken from the drawer and then
  replaced.  Another paperclip is taken from the
  drawer.  What is the probability that the first
  paperclip is red and the second paperclip is
  blue?
• 3/12 x 5/12 15/144 5/48

23

• Dependent the outcome of one event DOES effect
  the probability of another event
• Example Micah has five 1 bills, three 10
  bills, and two 20 bills in her wallet. She picks
  two bills at random. What is the probability of
  her picking the two 20 bills?
• 2/10 x 1/9 2/90 1/45

24

• Without Replacement DOES effect the probability
  of another event
• Example A bag contains 3 blue and 5 red marbles.
  Find the probability of drawing 2 blue marbles in
  a row without replacing the first marble.
• 3/8 x 2/7 6/56 3/28

25

• OR Probabilities Add the probabilities
• Example Rolling either a 5 or a 6 on a 1 6
  number cube.
• P(5 or 6)
•  
• 1/6 1/6 2/6 1/3
•  Example 2 Choosing either an A or an E from the
  letters in the word mathematics.
•  
• P(A or E)
• 2/11 1/11 3/11

26
1. Spinning red or green on a spinner that has 4
sections (1 red, 1green, 1 blue, 1 yellow)   ¼
¼ 2/4 ½   2. Drawing a black marble or a red
marble from a bag that contains 4 white, 3 black,
and 2 red marbles.   3/9 2/9 5/9  3.
Choosing either a number less than 3 or a number
greater than 12 from a set of cards numbered 1
20. 2/20 8/20 10/20 ½    
27

• AND Probabilities Multiply the probabilities
• Example 1 A die is rolled.  What is the
  probability that the number rolled is greater
  than 2 and even?
•  
• P( gt2 and Even)
•  
• Example 2 From a standard deck of cards, one
  card is drawn.  What is the probability that the
  card is black and a jack?
•  
•