Question

New Authors Established Authors Total Successful 17 13 30 Unsuccessful 18 2 20 Total 35 15 50 Consider the following events: S: an author is successful; U: an author is unsuccessful; N: an author is new; and E: an author is established. Describe the events in U and NU U in words. NnU is the event that an author is ---Select--- either new or unsuccessful established and unsuccessful either new or successful new and successful new and unsuccessful. NU U is the event that an author is ---Select--- either new or successful either established or unsuccessful either new or unsuccessful established and successful new and successful. Use the table to compute n( NU) and n(NU U). n(N NU) = n(N 2 U) =

Answer 1

N is for New . U is for unsuccesful .

$\large \cap \;\;means \; \;and$

$\large \cup \;\;means \; \;or$

so

$\large N \cap U\;$ is the event that author is New and unsuccesful .

$\large N \cup U\;$  is the event that author is either New or Unsuccesful .

new and succesful are all auther which are new and also unsuccesful . from table this is 18 authors . so

$\large \boldsymbol{n(N \cap U\;)=18}$

either new or unsuccesful include all auther which is new or unsuccesful . here we have 35 new author and 2 author which is not new but unsuccesful . so total number of either new or unsuccesful = 35+2=37

$\large \boldsymbol{n(N \cup U\;)=37}$