Posted by **student** on Monday, July 16, 2007 at 12:33am.

what is the probability that at least 2 students in a class of 36 have the same birthday?

Do i punch this in to the calculator or how did you found this way or method for your solution:

Log(365!) = 1792.3316

Log(329!) = 1581.7202

36 Log(365) = 212.3963

And therefore:

365!/[(365-36)! 365^36] =

Exp[1803.9383 - 1581.7202 - 212.3963] =

Exp[-1.7849] = 0.16781

1 - 0.16781 = 0.83219

THAT IS THE SOLUTION BUT I WANT TO UNDERSTAND THE STEPS FOR IT...CAN SOMEONE EXPLAIN THEM TO ME PLEASE...

Start with any student, he/she obviously will have a birthday (365/365 or probability is 1)

Now conider the second student. The probability that he/she will have a DIFFERENT birthday is (365/365)(364/365).

Now the third student's probability of having a DIFFERENT birthday is

(365/365)(364/365)(363/365)

Continuing this argument until we reach the last student to have a different birthday from all the rest we have

(329/365)(330/365)....(364/365)(365/365)

This is the probability that everybody will have a DIFFERENT birthday, so the the probability of NOT DIFFERENT, or at least somebody having the same birthday is 1 - the above multiplication.

I will let you finish the actual calculation.

yha um can you help me with my math

## Answer This Question

## Related Questions

- math, help - I need help or hint on the setup: what is the probability that at ...
- Math - Data Management - What is the probability that there are at least two ...
- math - the smallest number of people in a room where the probability of two of ...
- Statistics - Suppose 52 of the students in class have a calculator and 14 have a...
- Math Probability - A math class has 20 students who choose a topic from a list ...
- math - the smallest number of people in a room where the probability of two of ...
- probability - What is the probability that 2 out of 8 students will have the ...
- math - 1.If john served fruit punch in 8 ounce cups to a class on Monday. Mr. ...
- math/probability - For some reason I can not get my head around probability. ...
- math - 1.If john served fruit punch in 8 ounce cups to a class on Monday. Mr. ...

More Related Questions