Page 38 - Math SL HB Sem 3
P. 38

> lndependent  events

                 lndependenteventsareeventsthattheoccurrenceofonewouldnotinfluenceonthelikelihoodof
                 others'- That is,

                                                   P(AIB)    -  P(A)

                 Hence,
                                            P(A^B)-P(AIB)xP(B)
                                                        -  P(A) x P(B)


                       Watch  Out:

                Two events being mutually exclusive does  not imply an independence  I
                between  two events,  vice versa.                                      I
                                                                                    I       tl
                                                                                    I  I  t   I
                                                                                 I
                                                                                          I      I



                   \. Exainple:
                                 4222
                   Given P (A)  =   P(B) = - and P(/ u B)  =  n
                                 6,
                    Show that events A and B are independent.




















                  $   lntegrated  problem:

                    Example:

                   Given the events.A  and B are independent  and that
                                             P(e) = 5Pisl and P(A u B) =  0.71

                   a) Find P(B).
                   b) lllustrate  all the information  with a Venn diagram.

                    Solution:























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