Warm-Up

1
Warm-Up
1) In which year(s) did the team lose more games
than they won? 2) In which year did the team play
the most games? 3) In which year did the team
play ten games?
10
8
6
Number of Games
4
2
0
1
2
3
4
Year
2
Math IDay 48 (10-19-09)
UNIT QUESTION How do you use probability to make
plans and predict for the future? Standard
MM1D1-3 Todays Question How many different
outfits can you create? Standard MM1D1.a.
3
Probability

• GPS Algebra
• September 22, 2011

4
Statistics
5
Box Plots
6
Control Charts
7
Suppose you have a four color spinner red,
blue, green, and yellow.
8
Lets work on some definitions

• Experiment- is a situation involving chance
  that leads to results called outcomes.
• An outcome is the result of a single trial of an
  experiment
• An event is one or more outcomes of an
  experiment.
• Probability is the measure of how likely an event
  is.

• In the previous problem, the experiment is
  spinning the spinner.
• The possible outcomes are landing on yellow,
  blue, red or green
• One event of this experiment is landing on blue.
• The probability of landing on blue is one fourth.

9
Probability of an event

• The probability of event A is the number of ways
  event A can occur divided by the total number of
  possible outcomes.
• P(A)The number of ways an event can occur
• Total number of possible outcomes
• P(blue) number of ways to land on blue
• total number of colors

10
Probability
If P 0, then the event _______ occur.
cannot
It is ________
impossible
If P 1, then the event _____ occur.
must
It is ______
certain
So probability is always a number between ____
and ____.
1
0
11
Complements
All of the probabilities must add up to 100 or
1.0 in decimal form.
Example Classroom P (picking a boy)
0.60 P (picking a girl) ____
0.40
12
A glass jar contains 6 red, 5 green, 8 blue and 3
yellow marbles.Experiment A marble chosen at
random.

• Possible outcomes choosing a red, blue, green or
  yellow marble.
• Probabilities
• P(red) number of ways to choose red 6 3
• total number of marbles
  22 11
• P(green) 5/22, P(blue) ?, P(yellow) ?

13
Ex.
You roll a six-sided die whose sides are numbered
from 1 through 6. What is the probability of
rolling an ODD number?
There are 3 ways to roll an odd number 1, 3, 5.
P
14
Theoretical or experimental?

• We can calculate what our probabilities should be
  (theoretical values), but that is not always what
  happens in a real experiment. We could spin the
  spinner and land on the blue sector every time
  (experimental values).
• Thats not very likely, but it could happen

15
Favorable outcomes

• Suppose you have the four color spinner-(red,
  blue, green and yellow. The probability of
  spinning a red is ¼, but how many reds should you
  get if you spin it 20 times?
• 20 ¼ 5 times , you should theoretically land
  on red 5 times in 20 spins.
• Does that always happen with the spinners-why
  dont the values always match what you expect?

16
Tree Diagrams

• Tree diagrams allow us to see all possible
  outcomes of an event and calculate their
  probabilities.
• This tree diagram shows the probabilities of
  results of flipping three coins.
• Calculate P (heads), P(2heads,1 tail), P(tails)

17
Probability
Counting Principle
18
1. Your school cafeteria offers chicken or tuna
sandwiches chips or fruit and milk, apple
juice, or orange juice. If you purchase one
sandwich, one side item and one drink, how many
different lunches can you choose?
There are 12 possible lunches.
Sandwich(2) Side Item(2) Drink(3) Outcomes
chicken tuna
19
Multiplication Counting Principle

• At a sporting goods store, skateboards are
  available in 8 different deck designs. Each deck
  design is available with 4 different wheel
  assemblies. How many skateboard choices does the
  store offer?

32
20
Multiplication Counting Principle

• A father takes his son, Marcus, to Wendys for
  lunch. He tells Marcus he can get a 5 piece
  nuggets, a spicy chicken sandwich, or a single
  for the main entrée. For sides, he can get
  fries, a side salad, potato, or chili. And for
  drinks, he can get a frosty, coke, sprite, or an
  orange drink. How many options for meals does
  Marcus have?

48