Exclude leap years from the following calculations. (a) Compute the 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. (c) Compute the 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.

Question

Mathematics

Yates

24 November, 17:26

Exclude leap years from the following calculations. (a) Compute the 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. (c) Compute the 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.

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Gilbert Merritt · Answer 1

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.

Step-by-step 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.