Answer
P(not the 1st day of a month) $=\frac{353}{365}\approx0.967$
Work Step by Step
The sample space: a year (365 days). So, N(S) = 365.
The event "a person does not have a birthday on the 1st day of a month" is the complement of "a person has a birthday on the 1st day of a month".
Event = "a person has a birthday on the 1st day of a month" = {Jan 1, Feb 1, Mar 1, Apr 1, May 1, Jun 1, Jul, 1, Aug 1, Sep 1, Oct 1, Nov 1, Dec 1}. So, N(1st day of a month) = 12.
P(not the 1st day of a month) = 1 - P(1st day of a month) =
$1-\frac{N(\text{1st day of a month})}{N(S)}=\frac{365}{365}-\frac{12}{365}=\frac{353}{365}\approx0.967$
