Page 262 - Probability Demystified
P. 262

252                                                                APPENDIX

                                        Given that an alternator is defective, find the probability that it came
                                        from Supplier B.
                                     3. Two manufacturers supply paper cups to a catering service. Manu-
                                        facturer A supplied 100 packages and 5 were damaged. Manufacturer B
                                        supplied 50 packages and 3 were damaged. If a package is damaged,
                                        find the probability that it came from Manufacturer A.
                                     4. Box 1 contains 10 balls; 7 are marked ‘‘win’’ and 3 are marked ‘‘lose.’’
                                        Box 2 contains 10 balls; 3 are marked ‘‘win’’ and 7 are marked ‘‘lose.’’
                                        You roll a die. If you get a 1 or 2, you select Box 1 and draw a ball.
                                        If you roll 3, 4, 5, or 6, you select Box 2 and draw a ball. Find the
                                        probability that Box 2 was selected if you have selected a ‘‘win.’’
                                     5. Using the information in Exercise 4, find the probability that Box 1
                                        was selected if a ‘‘lose’’ was drawn.



                                 ANSWERS

                                                1             6   3          1             5   1
                                     1. PðB1Þ¼ ; pðGjB1Þ¼       ¼ ; PðB2Þ¼ ; PðGjB2Þ¼        ¼
                                                2            10   5          2            10   2

                                                           PðB1Þ  PðGjB1Þ
                                        PðB1jGÞ¼
                                                  PðB1Þ  PðGjB1Þþ PðB2Þ  PðGjB2Þ

                                                      1 3         3

                                                      2 5        10      6
                                                ¼            ¼        ¼
                                                  1 3    1 1    3   1   11
                                                      þ           þ
                                                  2 5    2 2   10   4
                                               150                                250
                                     2. PðAÞ¼      ¼ 0:375; PðDjAÞ¼ 0:02; PðBÞ¼      ¼ 0:625
                                               400                                400


                                        PðDjBÞ¼ 0:03
                                                         PðBÞ  PðDjBÞ
                                        PðBjDÞ¼
                                                 PðBÞ  PðDjBÞþ PðAÞ  PðDjAÞ
                                                         ð0:625Þð0:03Þ
                                               ¼                            ¼ 0:714
                                                 ð0:625Þð0:03Þþ ð0:375Þð0:02Þ
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