Answer:
[tex](a) = \frac{144}{133225} \\\\(b) = \frac{1}{365}[/tex]
Step-by-step 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).
[tex]=\frac{12}{365} X\frac{12}{365} = \frac{144}{133225}[/tex]
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):
[tex]= \frac{365}{365} X \frac{364}{365} =\frac{364}{365}[/tex]
P(2 people selected have birthday on the same day of same month) [tex]= 1-\frac{364}{365} \\\\= \frac{1}{365}[/tex]
