73. Consider n people and suppose that each of them has a birthday that is equally likely to be any of the 365 days of the year.

Furthermore, assume that their birthdays are independent, and let A be the event that no two of them share the same birthday. Define a

“trial” for each of theI mage pairs of people and say that trialI mage is a success if persons i and j have the same birthday. LetI mage be the event that trialI mage is a success.

(a) Find Image

(b) Are Image and Image independent when Image are all distinct?

(c) Are Image and Image independent when Image are all distinct?

(d) Are Imageindependent?

(e) Employ the Poisson paradigm to approximate Image

(f) Show that this approximation yields that Image when Image (g) Let B be the event that no three people have the same birthday. Approximate the value of n that makes Image.
(Whereas a simple combinatorial argument explicitly determines the exact determination of Image is very complicated.)
Hint: Define a trial for each triplet of people.