Answer:
a) There is a 99.73% chance that a randomly picked individual does not celebrate their birthday on March 14.
b) There is a 96.71% chance that a randomly picked individual does not celebrate their birthday on the 2nd day of any month.
c) There is a 98.08% chance that a randomly picked individual does not celebrate their birthday on the 31st day of a month.
d) There is a 92.33% chance that a randomly picked individual was not born in February.
Step-by-step explanation:
The probability is calculated as the number of successful outcomes divided by the total outcomes.
A standard year comprises 365 days.
(a) Calculating the probability that a randomly selected individual does not have a birthday on March 14:
Excluding March 14 yields 365-1 = 364 days. Thus,
364/365 = 0.9973
So, there is a 99.73% chance that a randomly selected person does not celebrate their birthday on March 14.
(b) Calculating the probability that a randomly selected person does not celebrate their birthday on the 2nd day of a month:
With 12 months, there are 12 occurrences of the 2nd day.
Thus,
(365-12)/365 = 0.9671
Hence, a 96.71% chance that someone does not have a birthday on the 2nd day of any month.
(c) Calculating the probability that a randomly chosen individual does not have a birthday on the 31st day of any month:
Months with 31 days include January, March, May, July, August, October, and December.
This totals 7 instances of the 31st day.
Thus,
(365-7)/365 = 0.9808
In conclusion, there's a 98.08% chance that a randomly selected person does not celebrate their birthday on the 31st day of any month.
(d) Calculating the probability that a randomly selected person was not born in February:
February has 28 days in a non-leap year. Thus,
(365-28)/365 = 0.9233
So, a 92.33% chance that a randomly picked individual was not born in February.
