Prob and stats Please answer all questions fully and show al

# 1, 10 pts Suppose that n people are selected at random from the JSU engineering programs. What is the chance that at least two of those n were born the same day ? Hint: Leap years are omitted)

Solution

from n people we have to choose atleast 2 people having same birthdate..
what is the probability that no 2 people have the same birthday?...

the first person can have any birthday. The second person\'s birthday has to be different. There are 364 different days to choose from, so the chance that two people have different birthdays is 364/365. That leaves 363 birthdays out of 365 open for the third person.

To find the probability that both the second person and the third person will have different birthdays, we have to multiply:

(365/365) * (364/365) * (363/365) = 132132/133225,
which is about 99.18%.

If we want to know the probability that four people will all have different birthdays, we multiply again:

(364/365) * (363/365) * (362/365) = 47 831 784/ 48 627 125,
or about 98.36%.

We can keep on going the same way as long as we want. A formula for the probability that n people have different birthdays is

If you know permutation notation, you can write this formula as

Prob( at least 2 one n were born on same day) = 1 - prob( no 2 of them were born on same day)
= 1 - (365_P_n)/(365^n)........