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EDEXCEL STATISTICS 1 PROBABILITY Exam Style Questions _ Worked

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					               EDEXCEL STATISTICS 1 PROBABILITY
              Exam Style Questions & Worked Solutions

Edexcel Exam Style Questions

1.   For the events A and B,

     P (A    B') = 0.32           P(A'   B ) = 0.11          and        P(A   B)=
     0.65

     (a)    Draw a Venn diagram to illustrate the complete sample space for
            the events A and B.
                                                                                      (3)

     (b)    Write down the value of P(A) and the value of P(B).
                                                                                      (3)

     (c)    Find P(A B').
                                                                                      (2)
     (d)    Determine whether or not A and B are independent.
                                                                                      (3)
                                                                         (Total 11 marks)

Worked Solution

      (a)


                           A                                       B


                               0.32      0.22         0.11


                                                                       0.35



     Hint:  P ( A B ) = 0.65 means A or B or both is the sum of all the
     numbers in A, B

     (b)       P(A) = 0.54     P(B) = 0.33



                         P ( A B¹)
     (c)       P ( A|B¹)
                             P (B¹)
                     0.32
                     0.67
                     0.478 (3 SF)




                                      Page 1 of 8
         EDEXCEL STATISTICS 1 PROBABILITY
        Exam Style Questions & Worked Solutions


(d)   P(A) = 0.54                P(B) = 0.33

      P(A) x P(B)= 0.54 x 0.33

                  = 0.1782

      P(A    B )= 0.22



      P( A   B)     P( A) P(B)

      Therefore the events A,B are not independent




                                 Page 2 of 8
                   EDEXCEL STATISTICS 1 PROBABILITY
                  Exam Style Questions & Worked Solutions



2.      A tennis player has two matches coming up. He estimates that the
        probability of him winning the first match is 0.5, the probability of
        winning the second match is 0.3 and the probability of winning both is 0.2

        (a)     Find the probability that he does not win either.
                                                                                        (3)

        (b)     Find the probability that he wins exactly one match.
                                                                                        (2)

        (c)     Given that he does not win the first match, find the probability that
                he wins the second.
                                                                                        (2)

        (d)     Determine whether winning the first match and winning the second
                are independent events.
                                                                                       (3)
                                                                          (Total 10 marks)

                           Win1st                           Win2nd


                                     0.3        0.2   0.1

                                                                    0.4



Reading the results directly off the Venn diagram

(a)       P( Does not win either ) 0.4

(b)       P(Wins exactly one )        0.3 0.1
                                      0.4

                           P (w 2 w1¹)
(c)       P (w 2 | w1¹)
                              P (w1¹)
                 0.1
                 0.5
                 0.2
(d)     P (W1   W2 ) 0.2
      P (W1) P (W2 )      0.5 0.3
                          0.15
        P (W1   W2 )      P (W1) P (W2 )
                          Not independent


                                            Page 3 of 8
                  EDEXCEL STATISTICS 1 PROBABILITY
                 Exam Style Questions & Worked Solutions


3.    A company assembles computers using components from two sources.
      Goodgear supplies 85% of the components and Buyrite supplies the rest.
      It is known that 3% of the components supplied by Goodgear are faulty
      and 6% of those supplied by Buyrite are faulty.

      (a)    Represent this information on a tree diagram.
                                                                                         (3)

      An assembled computer is selected at random.

      (b)    Find the probability that it is not faulty.
                                                                                         (3)
                                                                             (Total 6 marks)




(a)    Let G= Produced by Goodgear                    Let B= Produced by Buyrite
       Let F = Faulty component


                                                                        F
                                                            0.03



                               0.85               G
                                                            0.97
                                                                        F’

                                                            0.06        F

                               0.15               B


                                                             0.94       F’



(b)     P (F¹)   P (G   F¹) P (B      F¹)
                 P (G ).P (F¹|G ) P (B).P(F¹|B)
                 085 0.97 0.15 94
                 0.966 ( 3 SF )




                                            Page 4 of 8
               EDEXCEL STATISTICS 1 PROBABILITY
              Exam Style Questions & Worked Solutions



4.    A group of 100 young people were asked which teen magazine they
      enjoyed reading. 30 said they read Anna, 26 read Beat, 21 read Chillout,
      5 said they read both Anna and Beat, 7 both Beat and Chillout, 6 read
      both Chillout and Anna, and 2 said that they read all 3.

      (a)   Represent these data on a Venn diagram.
                                                                                  (6)

      A person was selected at random from this group.

      Find the probability that this person reads

      (b)   at least one of the magazines
                                                                                  (2)

      (c)   only Anna
                                                                                  (1)
      (d)   only one of the magazines
                                                                                  (2)

      (e)   Anna, given that he reads only one of the magazines
                                                                                  (3)
                                                                     (Total 13 marks)

(a)




                 A                                               B


                          21                3           16
                           C
                           C




                                            2
                                                    5
                                  4



                                            10
               39
                                                             C
                                                             C




                                      Page 5 of 8
             EDEXCEL STATISTICS 1 PROBABILITY
            Exam Style Questions & Worked Solutions

                              61
(b)   P( At least one )
                             100

                        21
(c)   P( Only A )
                       100

                        21 16 10
(d)   P ( Only one )
                            100
                         47
                        100

                                   21
(e)   P( A given only one )
                                   47




                                        Page 6 of 8
               EDEXCEL STATISTICS 1 PROBABILITY
              Exam Style Questions & Worked Solutions



5.    A teacher calculates that if a student regularly completes their
      homework then the probability that they will pass the end of unit test is
      0.9, but if the student fails to do homework the probability of passing is
      only 0.3. The teacher notes that only 75% of students regularly do their
      homework.

      A student was selected at random from this group.

      Find the probability that this student

      (a)   does not do homework and passes the exam
                                                                                   (2)

      (b)   passes the exam
                                                                                   (3)


      (c)   Given that the student actually failed the exam, what is the
            probability that they in fact regularly completed their homework
                                                                                 (4)
                                                                     (Total 9 marks)

(a)    Let H= Student completes homework              P= Passes unit test



                                                            P
                                               0.9



                    0.75           H
                                               0.1
                                                           P’

                                               0.3         P

                    0.25           H’


                                                0.7        P’




                                       Page 7 of 8
       EDEXCEL STATISTICS 1 PROBABILITY
      Exam Style Questions & Worked Solutions


(a)      P (H¹      P)    P (H¹).P(P|H¹)
                          0.25 0.3
                          0.075

(b)      P (P )    P (H    P ) P (H¹       P)
                   P (H ).P (P|H ) P (H¹).P (P|H¹)
                   0.75 0.9 0.25 0.3
                   0.75

                       P (H P¹)
(c)      P (H|P¹)
                          P (P¹)
                  0.75 0.1
                     0.25
                  0.3




                               Page 8 of 8

				
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