Discuss with your neighbor

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Discuss with your neighbor

• What do you know about probability??
• What are some real life examples that use
  probability?

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• Coin flip in sports
• Spinners and dice in board games
• Odds of survival in medical situations
• Insurance
• Predicting the weather
• Guessing on a multiple choice tests
• Gambling

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Probability

• EQ How do you calculate the
• probability of an outcome?

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Definition

• Probability is a number between 0 and 1 (or 0
  and 100) that describes how likely an event is
  to occur.

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To find probability

• Make a fraction
• What you want on top and
• total things that could happen on bottom
• Ex What is the probability of getting heads when
  you flip a coin?
• 1 on top (what you want can happen once)
• 2 on bottom (it could be heads or tails)
• P(heads) ½

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Try it

• What is the probability of getting a 2 when you
  roll a die?
• 1/6
• What is the probability of getting an odd number?
• 3/6 ½

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Certain vs. Impossible

• If something is certain, what does that mean?
• If something is impossible, what does that mean?

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Think about it

1. Name something that is impossible.
2. Name something that is certain.

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Discuss with a partner

• What is a tree diagram?
• Talk about how to make one for this situation
• Dan is buying 2 snacks. He can choose from 3
  different candy bars and 4 types of chips.

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The Problem

• You need to buy a shirt and tie for a special
  occasion. Your choices are shown below.
• Use a tree diagram to find how many combinations
  of a shirt and tie are possible.

off-white
white
Solid blue
Blue with pin stripes
White with pin stripes
navy
blue
yellow
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Use a Tree Diagram to Solve
OW
W
SB
BP
WP
There are 15 combinations!
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What is the probability of choosing a solid white
shirt and blue tie?
OW
W
SB
BP
WP
P(SW B) 1 out of 15 or 1/15
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Another way to find the number of combinations

• THE COUNTING PRINCIPLE!!

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The Counting Principle

• You can count the 3 ties for each shirt (5 shirts
  total)
• OR
• You can multiply
• 5 shirts 3 ties
• 15 combinations!

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Use the counting principle

• Mrs. Spanier flips a coin and then rolls a die.
  How many possible combinations can occur?
• 12
• Now Mrs. Spanier flips a coin, and then ANOTHER
  coin, and then rolls a die. How many possible
  combinations can occur?
• 24

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ONE more way to find the possible outcomes of
multiple events

• A systematic or organized list!!!
• Like a tree diagram without the branches.
• You can abbreviate and use a key.

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Mrs. Miller flips a coin two times, and then
rolls a die. How many possible combinations can
occur?

• If you start with heads, and then heads
• Make a list for what you can then spin.

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Now list heads then tails

• H H 1 H T 1
• H H 2 H T 2H H 3 H T 3
• H H 4 H T 4
• H H 5 H T 5
• H H 6 H T 6
• Finish the list!
• Do you get 24 combinations?

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Lets Practice!
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• Use the COUNTING principle to find the possible
  number of combinations
• You are going to get an ice cream cone. There are
  6 flavors of ice cream and 3 different cones.
• You are buying a car. There are 2 body styles, 5
  colors, and 3 models to choose from.

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• Use a TREE DIAGRAM to find the possible number of
  combinations
• You are picking out an outfit. You have 3 shirts
  (red, orange, and yellow) and 4 different pants
  (jeans, sweats, shorts, dressy) to choose from.

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• What is probability that if I pick a person at
  random from this classroom, that I will pick
• A boy?
• Someone with shorts on?
• An alien?