Question

Consider two people being randomly selected. (For simplicity, ignore leap years.)

Answer 1

Answer:

A)144/133225

B)1/365

Step-by-step explanation:

A) We want to find the probability that two people have a birthday on the 18th of any month.

If we Neglect leap year like the question says, it means that there are 365 days in a year.

Now, we have 12 possible number of 18th day in all months that make a calendar year.

Thus;

If two people have birthday on 18th, the probability that the two of them will have birthday on the 18th of any month is;

P(both to have birthday on the 18th of any month) = (12/365) × (12/365) = 144/133225

B) We want to find the probability that two people have a birthday on the same day of the same month. This can be written as;

P(2 people have a birthday on the same day of the same month) + P(2 people do not having birthday on same day of same month) = 1

Probability of 2 people not having birthday on same day of same month = 365/365 × 364/365 = 364/365

P(2 people have a birthday on the same day of the same month) = 1 - (364/365) = 1/365