Answer:
a) 99.73% probability that a randomly selected person does not have a birthday on March 14.
b) 96.71% probability that a randomly selected person does not have a birthday on the 2 nd day of a month.
c) 98.08% probability that a randomly selected person does not have a birthday on the 31 st day of a month.
d) 92.33% probability that a randomly selected person was not born in February.
Explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
A non-leap year has 365 days.
(a) Compute the probability that a randomly selected person does not have a birthday on March 14.
There are 365-1 = 364 days that are not March 14. So
364/365 = 0.9973
99.73% probability that a randomly selected person does not have a birthday on March 14.
(b) Compute the probability that a randomly selected person does not have a birthday on the 2 nd day of a month.
There are 12 months, so there are 12 2nds of a month.
So
(365-12)/365 = 0.9671
96.71% probability that a randomly selected person does not have a birthday on the 2 nd day of a month.
(c) Compute the probability that a randomly selected person does not have a birthday on the 31 st day of a month.
The following months have 31 days: January, March, May, July, August, October, December.
So there are 7 31st days of a month during a year.
Then
(365-7)/365 = 0.9808
98.08% probability that a randomly selected person does not have a birthday on the 31 st day of a month.
(d) Compute the probability that a randomly selected person was not born in February.
During a non-leap year, February has 28 days. So
(365-28)/365 = 0.9233
92.33% probability that a randomly selected person was not born in February.