Page 211 - Math Course 3 (Book 2)
P. 211

Probability of Compound Events




                                                                  Dependent Events
                             Let’s Begin
                                                                     Example



               Independent Events                                  At the school carnival, winners in the ring-toss
                                                                   game are randomly given a prize from a bag that
                   Example                                         contains 4 sunglasses, 6 hairbrushes, and 5 key
                                                                   chains. Three prizes are randomly drawn from the
                                                                   bag and not replaced.

                 TRAVEL                                            Find P(sunglasses, hairbrush, key chain).
                 Rae is flying from Birmingham to Chicago. On the
                 first leg of her trip, she has to fly from Birmingham
                 to Houston. In Houston, she changes planes and
                 heads on to Chicago. The airline reports that the
                 flight from Birmingham to Houston has a 90% on-
                 time record, and the flight from Houston to Chica-
                 go has a 50% on-time record. What is the probabili-
                 ty that both flights will be on time?






                                                                   The selection of the first prize affects the selection
                                                                   of the next prize since there is one less prize from
                                                                   which to choose. So, the events are dependent.


                           P(A and B) = P(A) • P(B)   Probability of    First Prize:
                                             independent                             4  ←number of sunglasses
                                             events                 P(sunglasses) =  15  ←total number of prizes

                 P(B-H on time  =   P(B-H on time) • P(H-C on time)
                  and H-C on                                        Second Prize:
                                                                                  6
                     time)                                          P(hairbrush) =        or  3  ←number of hairbrush
                                =             0.9        •           0.5         14    7  ←total number of prizes
                                            90% = 0.9 and 50% = 0.5
                                                                    Third Prize:
                                                                                  5
                                = 0.45        Multiply.             P(key chain) =          ←number of key chains
                                                                                 13  ←total number of prizes

                                The probability that both flights   P(sunglasses, hairbrush, key chain) =
                   Answer                                          P(sunglasses) • P(hairbrush) • P(key chain)
                                    will be on time is 45%.

                                                                        4            3             5
                                                                   =                     •                           •  13  Substitution
                                                                       15
                                                                                     7
                                                                      60       4
                                                                   =              or   Multiply
                                                                     1365     91          Substitution

                                                                                    The probability of drawing
                                                                      Answer       sunglasses a hairbrush, and a
                                                                                                    4
                                                                                        key chain is         .
                                                                                                   91



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