PROBABILITY

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PROBABILITY

• Experimental vs. Theoretical

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What is Probability?

• Probability is a number from 0 to 1 that tells
  you how likely something is to happen.
• Probability can be either theoretical or
  experimental.

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Probability

• THEORETICAL
• Theoretical probability can be found without
  doing and experiment.

• EXPERIMENTAL
• Experimental probability is found by repeating an
  experiment and observing the outcomes.

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THEORETICAL PROBABILITY

• I have a quarterMy quarter has a heads side and
  a tails side
• Since my quarter has only 2 sides, there are only
  2 possible outcomes when I flip it. It will
  either land on heads, or tails

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THEORETICAL PROBABILITY

• When I flip my coin, the probability that my coin
  will land on heads is 1 in 2
• What is the probability that my coin will land on
  tails??

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Theoretical Probability

• Right!!! There is a 1 in 2 probability that my
  coin will land on tails!!!

• A probability of 1 in 2 can be written in three
  ways
• As a fraction ½
• As a decimal .50
• As a percent 50

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Theoretical probability

• When I spin this spinner, I have a 1 in 4 chance
  of landing on the section with the red A in it.

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A 1 in 4 chance can be written 3 ways
Theoretical Probability

• As a fraction ¼
• As a decimal .25
• As a percent 25

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Theoretical Probability
I have three marbles in a bag.
1 marble is red
1 marble is blue
1 marble is green

• I am going to take 1 marble from the bag.
• What is the probability that I will pick out a
  red marble?

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Theoretical Probability

• Since there are three marbles and only one is
  red, I have a 1 in 3 chance of picking out a red
  marble.
• I can write this in three ways
• As a fraction 1/3
• As a decimal .33
• As a percent 33

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Experimental Probability

• Experimental probability is found by repeating an
  experiment and observing the outcomes.

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Experimental Probability

• Remember the bag of marbles?
• The bag has only 1 red, 1 green, and 1 blue
  marble in it.
• There are a total of 3 marbles in the bag.
• Theoretical Probability says there is a 1 in 3
  chance of selecting a red, a green or a blue
  marble.

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Experimental Probability

• Draw 1 marble from the bag.

• It is a red marble.

• Record the outcome on the tally sheet

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Experimental Probability

• Put the red marble back in the bag and draw
  again.
• This time your drew a green marble.
• Record this outcome on the tally sheet.

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Experimental Probability

• Place the green marble back in the bag.
• Continue drawing marbles and recording outcomes
  until you have drawn 6 times. (remember to place
  each marble back in the bag before drawing again.)

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Experimental Probability

• After 6 draws your chart will look similar to
  this.
• Look at the red column.
• Of our 6 draws, we selected a red marble 2 times.

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Experimental Probability

• The experimental probability of drawing a red
  marble was 2 in 6.
• This can be expressed as a fraction 2/6 or 1/3
  a decimal .33 or a
  percentage 33

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Experimental Probability

• Notice the Experimental Probability of drawing a
  red, blue or green marble.

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Comparing Experimental and Theoretical Probability

• Look at the chart at the right.
• Is the experimental probability always the same
  as the theoretical probability?

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Comparing Experimental and Theoretical Probability

• In this experiment, the experimental and
  theoretical probabilities of selecting a red
  marble are equal.

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Comparing Experimental and Theoretical Probability

• The experimental probability of selecting a blue
  marble is less than the theoretical probability.
• The experimental probability of selecting a green
  marble is greater than the theoretical
  probability.

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Probability Review
Probability is a number from 0 to 1 that tells
you how likely something is to happen.
There are 2 types of probability

• Theoretical (can be found without doing an
  experiment)
• Experimental (can be found by repeating an
  experiment and recording outcomes.)

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Probability Review

• Probability can be expressed as a fraction, a
  decimal or a percentage.