Probability

1
Probability

• Students will be able to change fractions to
  percents, etc.
• Students will be able to find experimental and
  theoretical probabilities.

2
Converting to Percents

• To convert a decimal to a percent, multiply the
  decimal by 100.
• Example .25 ? .25 x 100 25
• To convert a fraction to a percent, convert to a
  decimal and then multiply by 100.
• Example ¼ ? 1 4 .25 ? .25 x 100 25

3
Converting Percents

• To convert a percent to a decimal, divide the
  percent by 100.
• Example 35 ? 35 100 .35
• To convert a percent to a fraction, put the
  percent over 100 and reduce fraction to lowest
  terms (use your calculator).
• Example 35 ?

4
What is Probability?

• A probability is expressed as a number between 0
  and 1 that tells how likely an event is to
  happen.
• A probability of 0 means that the event has no
  chance of happening. What is an example of an
  event that is impossible.

Walking on Jupiter tomorrow.
5
What is Probability?

• A probability of 1 means that an event is certain
  to occur. What would be an event that has a
  probability of 1?
• The sun coming up tomorrow.
• Any event that is between impossible and certain
  has a probability between 0 and 1, and so is
  usually written as a fraction.

6
Probability in Perspective

• In the California lottery, you pick 6 numbers
  from the numbers 1-50. If you match all 6
  numbers, you win!
• There are 18,009,460 possible number
  combi-nations. Here are some interesting facts

• If you filled out a card for each possible
  combinations, and if you could fill out those
  cards at the rate of one per second, it would
  take you 208 days (working 24 hours a day) to
  complete the task.

7
Probability in Perspective

• If you buy 50 Lotto tickets a week, you could
  expect to win the Jackpot once in 5,000 years.

• If you bought 2 Lotto tickets a week for 110,000
  years, you would have a 50 chance of winning the
  jackpot at least once.

• Some people sell books to help you have a better
  chance of winning You can increase your chance
  of winning 100! Of course, you can increase
  your chance of winning 100 by just buying 2
  tickets instead of 1!!

8
Probability in Perspective
The probability of winning the Lotto is about 1
in 18 million

• You are 18 times more likely to die from
  flesh-eating bacteria than to win the Lotto.

• You are 3600 times more likely to die of cancer
  from eating a peanut butter sandwich every day.

• You are 600 times more likely to die being struck
  by lightning.

• You are 28 times more likely to be dealt a royal
  flush during the opening hand of a card game.

9
Probability in Perspective

• You and a friend could visit the Empire State
  Building.
• One of you stays on the street and walks
  around the building holding a can, while the
  other goes to the top and throws off a coin.
  

You have a better
chance of that coin landing in that can
than you do of winning the lottery!
10
What is an Experiment?

• Rolling a die, flipping a coin, or spinning a
  spinner all of these are experiments.
• If you were to flip a coin 50 times and you got a
  head 30 times, the experimental probability would
  be 30/50 which is 3/5 in lowest terms or 0.6 in
  decimal form.

11
A Probability Experiment

• Spinning this spinner is an experiment. There
  are 3 possible outcomes.
• Suppose we spun the spinner 10 times and landed
  on green 6 times.
• What is the experimental probability that we
  would land on green on the next spin?

6 greens 10 spins
The probability is
12
Conduct an Experiment

• Now, lets conduct a probability experiment.
• Get your pencil ready to write down a number when
  I say.
• Write down a number from 1 through 4.
• Lets see what was chosen most frequently.
• Was it 3? Studies have shown that 3
  is the number written most
  frequently.
• What is the estimated probability that
  the people in this class chose
  3?

3
13
What Should Happen?

• If you were to toss a coin, how many possible
  outcomes are there?
• two
• Are each of these outcomes equally likely?
• yes
• Considering this, what should the probability be
  for tossing a head?

½
14
Theoretical Probability

• Theoretical Probabilities are determined by what
  should happen, ideally.
• When dealing with equally likely outcomes
• P(E)

Number of favorable outcomes
Total number of possible outcomes
15
Examples of Theoretical Probability

• Thus, the theoretical probability of tossing a
  Head, when flipping a coin is?
• The theoretical probability of tossing an odd
  number when tossing a die is?
• or ½

½
16
Sample Space

• The set of all possible outcomes of an experiment
  is called the sample space.
• When more than one event occurs, you need a way
  to find all the possible outcomes.
• The easiest way to do this is with a tree
  diagram.

17
Tree Diagram

• A person flips a nickel and then spins this
  spinner

(H, R) (H, G) (H, Y)
Red Green Yellow
H T
Red Green Yellow
(T, R) (T, G) (T, Y)