HELP!! Find the probability that at least two students in the class have same bdays

Question

A biology class has 3535 students. Find the probability that at least two students in the class have the same birthday. For? simplicity, assume that there are always 365 days in a year and that birth rates are constant throughout the year.? (Hint: First, determine the probability that no 2 students have the same birthday and then apply the complementation? rule.)

 

The approx probability is: (round to four decimal places

Answer 1

This is a classical problem that can be found in most texts.  The number 3535 is probably a typo.  Assuming that the class size is 35 we can proceed as follows.

 

Let B be the event that no two students share the same birthday.  The first person must have a birthday some day of the year and that probability is 365/365.  The second person cannot have the same birthday as the first person so that probability is 364/365.  The third person cannot have the same birthday as the other two so that probability is 363/365 and so on until we get to the 35th person.  Using the multiplication rule we have

 

P(B) = (365/365)(364/365)(363/365)...

 

Hint: Note the numerator is nothing more than a permutation.  Use the permutation feature of a calculator to get the top.  The denominator should be obvious it is 365 raise to some power which I let you figure out.

 

Once you have P(B) use 1 - P(B) to find the probability that at least two students share the same birthday.