Question

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

(a) What is the probability that two people have a birthday on the 9th of any month?
(b) What is the probability that two people have a birthday on the same day of the same month?

Answer 1

`(a) = (144)/(133225) \\\\(b) = (1)/(365)`

Explanation:

Part (a) the probability that two people have a birthday on the 9th of any month.

Neglecting leap year, there are 365 days in a year.

There are 12 possible 9th in months that make a year calendar.

If two people have birthday on 9th; P(1st person) and P(2nd person).

`=(12)/(365) X(12)/(365) = (144)/(133225)`

Part (b) the probability that two people have a birthday on the same day of the same month

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

P(2 people selected not having birthday on same day of same month):

`= (365)/(365) X (364)/(365) =(364)/(365)`

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