SOLUTION: What is probability that of three people selected at random at least two were born on the same day.

Algebra ->  Probability-and-statistics -> SOLUTION: What is probability that of three people selected at random at least two were born on the same day.       Log On


   

Question 1075827: What is probability that of three people selected at random at least two were born on the same day.
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
The complement event is for all of them to have different
birthdays.  Suppose they are Tom, Dick and Harry.

So we get the probability that they all have different 
birthdays.

There are 365 possible birthdays for Tom.
That leaves 364 possible birthdays for Dick.
That leaves 363 possible birthdays for Harry. 

So the number of ways they can all have different birthdays 
is 365%2A364%2A363

The number of ways they can have ANY birthdays, different
or not, is 365%2A365%2A365

So the probability that all three have different birthdays is

%28365%2A364%2A363%29%2F%28365%2A365%2A365%29=132132%2F133225

So the probability that at least two have the same birthday
is



Edwin