4 Alf and Mabel are members of a bowls club and sometimes attend the club's social events. The probability, \(\mathrm { P } ( A )\), that Alf attends a social event is 0.70 .
The probability, \(\mathrm { P } ( M )\), that Mabel attends a social event is 0.55 .
The probability, \(\mathrm { P } ( A \cap M )\), that both Alf and Mabel attend the same social event is 0.45 .

1. Find the probability that:
   1. either Alf or Mabel or both attend a particular social event;
   2. either Alf or Mabel but not both attend a particular social event.
2. Give a numerical justification for the following statement.
   "Events \(A\) and \(M\) are not independent."
3. Ben and Nora are also members of the bowls club and sometimes attend the club's social events. The probability, \(\mathrm { P } ( B )\), that Ben attends a social event is 0.85 .
   The probability, \(\mathrm { P } ( N )\), that Nora attends a social event is 0.65 .
   The attendance of each of Ben and Nora at a social event is independent of the attendance of all other members. Find the probability that:
   1. all four named members attend a particular social event;
   2. none of the four named members attend a particular social event.