Probability with tree diagram - Excel by tbp20087

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									                                            PROBABILITY USING TREE DIAGRAMS
                                  6        # Consider the sample space when three coins are tossed:


                                                                                       H HHH
                                                                     H                 T HHT
                                                    H
             n(S) = 8                                                T                 H HTH
                                                                                       T HTT
                                       0
                                                                                       H THH
                                                                    H
                                                                                       T THT
                                                    T
                                                                     T                 H TTH
                                                                                       T TTT
                                                 Coin 1            Coin 2        Coin 3

                               Find the following probabilities
                                       P(HHT / last two coins show HH)




r
◄                                                                                 1
Random no                                                                         2
                                                                                  3
                                                                                  4
                               LOOKUP("C",{"a","b","c","d";1,2,3,4}) equals 3     5
                                                                                  6
Gives qu no.                    ####                                              7
Writes question                 ####                                              8
                                                                                  9
Correct answer                   0.38                                             10
Compares your ans and ncorrect answer                                            11
                            No, Try again.                                       12
                                 P(HHT / last two coins show HH)                 13
                   P(HHT / last two coins show HH)
Equivalent expressions                                                           14
                   P(HHT / last two coins show HH)                               15
                              16
                              17
1   Correct. Well done.   4   18
2   Yes!                  5   19
3   Right!                    20
4   Well done!                21
5   Correct.                  22
                              23
1   No!                       24
2   Try again.                25
3   Not correct!
4   Have another try!
5   Wrong!
SING TREE DIAGRAMS
ce when three coins are tossed:
                 Possible outcomes

                 H HHH           *
H                T HHT           *

T                H HTH           *
                 T HTT           *

                 H THH           *
H
                 T THT           *
                 H TTH           *
T
                 T TTT           *
            Coin 3

                                          ANSWER

                                                        0
                                      \            Invisible answer

                                      d
                                      s




                 P(HHH)                             0.125    a
                 P(TTT)                             0.125    b
                 P(THT)                             0.125    c
                 P(at least one T)                  0.875    d
                 P(coin 1 = H)                         0.5   e
                 P(exactly two T)                   0.375    f
                 P(exactly two H)                   0.375    g
                 P(exactly one H)                   0.375    h
                 P(the last toss is a H)               0.5   I
                 P(TTT / at least two T)             0.25    j
                 P(TTT / at least one T)            0.143    k
                 P(TTT / at least two H)                 0   l
                 P(THH / at least one H)            0.143    m
                 P( last two tosses are T)           0.25    n
                 P( first two tosses are T)          0.25    o
P( last two tosses are H)          0.25   p
P( first two tosses are H)         0.25   q
P(at least one H)                 0.875   r
P(at least two H / at least one H)0.571   s
P(at least two T / at least one T)0.571   t
P(HHT / at least one H)           0.143   u
P(HHH / first two coins show HH)0.5       v
P(HHT / last two coins show HH) 0         x
P(HHH / at least one H)           0.143   y
P(HTH / at least two H)            0.25   z
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   Use  x
                                         PROBABILITY USING TREE DIAGRAMS
                                  24   # Assume that 5 % of males and 1 % of females are colourblind.
                                                    POSSIBLE
                                                    OUTCOMES                     PROBABILITIES
                                  0.05             C      MC         P(MC) = O.5 x 0.05 = 0.025
                        M
            0.5                  0.95              N      MN          P(MN) = O.5 x 0.95 = 0.475
      0

            0.5                    0.01             C     FC         P(FC) = O.5 x 0.01 = 0.005
                        F
                                    0.99            N      FN        P(FN) = O.5 x 0.99 = 0.495

                                            Tree diagram
                                A person is chosen at random and tested for colourblindness.

                                Find the following probabilities
                                        P(colourblind / female)




                                                                                  1
Random no                                                                         2
                                                                                  3
                                                                                  4
                                LOOKUP("C",{"a","b","c","d";1,2,3,4}) equals 3    5
                                                                                  6
Gives qu no.                     10                                               7
Writes question                 P(colourblind / female)                           8
                                                                                  9
Correct answer                  0.01                                              10
Compares your ans and ncorrect answer
                        Correct. Well done.
                                P(colourblind / female)
Equivalent expressions P(colourblind / female)
                       P(colourblind / female)
1   Correct. Well done.   5
2   Yes!                  4
3   Right!
4   Well done!
5   Correct.

1   No!
2   Try again.
3   Not correct!
4   Have another try!
5   Wrong!
SING TREE DIAGRAMS
es and 1 % of females are colourblind.
E
ES         PROBABILITIES
                                                 Colourblind Normal
  P(MC) = O.5 x 0.05 = 0.025
                                    Male            0.025       0.475      0.5
  P(MN) = O.5 x 0.95 = Female
                        0.475                       0.005       0.495      0.5
                                    Totals           0.03        0.97       1

 P(FC) = O.5 x 0.01 = 0.005
                                                 Two way table
  P(FN) = O.5 x 0.99 = 0.495
                                    It is sometimes easier to use the information
                                    in a two way table.
d tested for colourblindness.

                                        ANSWER

                                                       0.01
                                                 Invisible answer

                                    d
                                    s




                 P(a male)                                0.5
                 P(a female)                              0.5
                 P(a colourblind female)               0.005
                 P(a colourblind male)                 0.025
                 P(a colourblind person)                0.03
                 P(a person who is not colourblind)     0.97
                 P(female / colourblind)          0.1666667
                 P(male / colourblind)            0.8333333
                 P(colourblind / male)                  0.05
                 P(colourblind / female)                0.01

								
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