Probability

							Probability
Probability

   In this chapter will be:
   Certain, impossible or possible
   Equally likely outcomes
   Using numbers to represent probability
   Calculating probabilities
   The probability of something not
   happening
   Experimenting with probability
Probability


                    Lesson 1
                    Objective:
   To use the vocabulary of probability when
    interpreting the results of an experiment
Probability


                          Starter:
         Four people are taking part in a charity fun-run:
              Arthur, 63, a retired quantity surveyor,
                   Mabel, 24, a gym instructor,
      Gary, 12, a school pupil and computer games expert,
     Linford Christie, 37, three times world 100m champion.
Probability


                          Starter:
         Four people are taking part in a charity fun-run:
              Arthur, 63, a retired quantity surveyor,
                   Mabel, 24, a gym instructor,
      Gary, 12, a school pupil and computer games expert,
     Linford Christie, 37, three times world 100m champion.
            Who is most likely to win?
Probability


                          Starter:
         Four people are taking part in a charity fun-run:
              Arthur, 63, a retired quantity surveyor,
                   Mabel, 24, a gym instructor,
      Gary, 12, a school pupil and computer games expert,
     Linford Christie, 37, three times world 100m champion.
         Who is most likely to win?
        Who is likely to come second ?
Probability


                          Starter:
         Four people are taking part in a charity fun-run:
              Arthur, 63, a retired quantity surveyor,
                   Mabel, 24, a gym instructor,
      Gary, 12, a school pupil and computer games expert,
     Linford Christie, 37, three times world 100m champion.
         Who is most likely to win?
        Who is likely to come second ?
           Who is unlikely to win?
Probability


      Certain, impossible or possible?
Probability


      Certain, impossible or possible?
     To show probabilities we can use a
          likelihood scale, like this:
Probability


         Certain, impossible or possible?
        To show probabilities we can use a
             likelihood scale, like this:


   Impossible   Unlikely   Even chance   Likely   Certain
Probability


         Where is the likelihood of …
   (a) The next person to book a holiday will
                   be male?


   Impossible   Unlikely   Even chance   Likely   Certain
Probability


         Where is the likelihood of …
   (a) The next person to book a holiday will
                   be male?


   Impossible   Unlikely   Even chance   Likely   Certain
                             (a)
Probability


           Where is the likelihood of …
    (b) It will snow in Australia on Christmas
                   Day this year?


   Impossible   Unlikely   Even chance   Likely   Certain
                             (a)
Probability


           Where is the likelihood of …
    (b) It will snow in Australia on Christmas
                   Day this year?


   Impossible   Unlikely   Even chance   Likely   Certain
                  (b)        (a)
Probability


           Where is the likelihood of …
      (c) A woman will captain the women’s
                  rugby team?


   Impossible   Unlikely   Even chance   Likely   Certain
                  (b)        (a)
Probability


           Where is the likelihood of …
      (c) A woman will captain the women’s
                  rugby team?


   Impossible   Unlikely   Even chance   Likely   Certain
                  (b)        (a)                   (c)
Probability


             Where is the likelihood of …
           (d) A train will be late tomorrow?



   Impossible   Unlikely   Even chance   Likely   Certain
                  (b)        (a)                   (c)
Probability


             Where is the likelihood of …
           (d) A train will be late tomorrow?



   Impossible   Unlikely   Even chance   Likely   Certain
                  (b)        (a)         (d)       (c)
Probability


          Where is the likelihood of …
    (e) You can learn Japanese in one day?



   Impossible   Unlikely   Even chance   Likely   Certain
                  (b)        (a)         (d)       (c)
Probability


          Where is the likelihood of …
    (e) You can learn Japanese in one day?



   Impossible   Unlikely   Even chance   Likely   Certain
     (e)          (b)        (a)         (d)       (c)
Probability


                           Now try …




   Impossible   Unlikely     Even chance   Likely   Certain
     (e)          (b)          (a)         (d)       (c)
Probability


   Using numbers to represent probabilities
The Probability Scale


0                           0.5                          1
Impossible                 Evens                   Certain

   Draw a line 10cm long and mark off every centimetre.
The Probability Scale


0                         0.5                          1
Impossible               Evens                   Certain

 Draw a line 10cm long and mark off every centimetre.
 0, for impossible, is marked at the left hand end.
The Probability Scale


0                         0.5                          1
Impossible               Evens                   Certain

 Draw a line 10cm long and mark off every centimetre.
 0, for impossible, is marked at the left hand end.
 0.5, for evens, is marked in the middle.
The Probability Scale


0                         0.5                          1
Impossible               Evens                   Certain

 Draw a line 10cm long and mark off every centimetre.
 0, for impossible, is marked at the left hand end.
 0.5, for evens, is marked in the middle
 1, for certain, is marked at the right hand end.
The Probability Scale


0                          50                        100
Impossible                Evens                   Certain

   Certain can also be called 100% and evens, 50%.
The Probability Scale


0                       0.5          1
Impossible             Evens   Certain

   Now do some questions…
Probability


                    Lesson 1
                    Plenary:
   Probability uses numbers to represent the
      chance that something will happen
Probability


                     Lesson 1
                      Plenary:
   Probability uses numbers to represent the
       chance that something will happen
    All probabilities have a value from 0 to 1
                 (or 0% to 100%)
Probability


                     Lesson 1
                      Plenary:
   Probability uses numbers to represent the
       chance that something will happen
    All probabilities have a value from 0 to 1
                 (or 0% to 100%)
     Probabilities can be represented on a
                       scale
THE END
Probability


                   Lesson 2
                  Objective:
   To find and record all possible outcomes
    for single events in a systematic way.
Probability


         Events and Outcomes
                  Starter
List all the outcomes for the following events:
List all the outcomes for the following events:

   Choosing a person from
    this group
List all the outcomes for the following events:

   Choosing a fruit
List all the outcomes for the following events:

   Throwing one die
List all the outcomes for the following events:

 Throwing one die
 Throwing both dice
List all the outcomes for the following events:

   Choosing a card from
    this hand
Probability


              Now try …
Probability


        Calculating Probabilities
What is the probability of …

   Throwing a 3 with one
    die?
What is the probability of …

 Throwing a 3 with one
  die?
 Throwing an odd
  number?
What is the probability of …

 Throwing a 3 with one
  die?
 Throwing an odd
  number?
 Throwing seven with two
  dice?
What is the probability of …

 Throwing a 3 with one
  die?
 Throwing an odd
  number?
 Throwing seven with two
  dice?
 Throwing fifteen with two
  dice?
What is the probability of …

   Choosing a face card
    from this hand?
What is the probability of …

 Choosing a face card
  from this hand?
 Choosing a red card
  from this hand?
What is the probability of …

   Choosing a yellow
    crayon?
What is the probability of …

   Hitting a number in the
    three times table (a
    multiple of three)?
What is the probability of …

   Choosing a vowel from
    this sign?
Probability


              Now try …
Probability


        Probabilities that add to 1
What is the probability of …

   Not throwing a 3 with
    one die?
What is the probability of …

   Not choosing a face card
    from this hand?
What is the probability of …

   Not choosing a yellow
    crayon?
What is the probability of …

   Choosing a consonant
    (not a vowel) from this
    sign?
Probability



              Remember:
      The probability of something not
                happening is
      1 – the probability it will happen
Probability


              Now try …
Probability


      Experimenting with probability
Probability


      What experiment shall we do?
Probability



      Copy the results into your book
Probability



            Copy the table into your book



   Result           Tally         Frequency
   Heads
   Tails
Probability


     Toss a coin ten times and record the
             results in your table.
   Result        Tally         Frequency
   Heads
   Tails
Probability


     Toss a coin ten times and record the
             results in your table.
   Result           Tally             Frequency
   Heads
   Tails
   Use these results to calculate the experimental
   And theoretical probability of landing on heads.
Probability


        Now try some questions
Probability - Plenary

   In this chapter we have looked at:
   Certain, impossible or possible
   Equally likely outcomes
   Using numbers to represent probability
   Calculating probabilities
   The probability of something not
   happening
   Experimenting with probability
Probability - Plenary

   In this chapter we have looked at:
   Certain, impossible or possible
   Equally likely outcomes
   Using numbers to represent probability
   Calculating probabilities
   The probability of something not
   happening
   Experimenting with probability
   Do you understand all of these topics?
Probability


                  Homework:
        Revise all of the new material
            for a test next lesson.
      To do this you should produce at
     least half a page of revision notes.
Probability




      THE END
Probability