Hi everybody,

first reply for me, here. Linux and math fan, so:

about the 'birthday' question of the Cambridge test, here is my modest explanation:

If we have 3 guests, the probability that a fourth one has another birthday than the 3 others is P:

prob that she is not born the same day than the first: 364/365

and that she is not born the same day than the second: 363/365

and that she is not born the same day than the third: 362/365

simultaneously, so: P =364/365 * 363/365 * 362/365

The probability this fourth one has the same birthday as one

of the 3 others is, complementary: 1-P

If we have n guests, P =364/365 * 363/365* ... * (366-n)/365

Now we have to find n as 1-P >= 1/2 or P <= 1/2

5 lines of Python code give n =23 (1-P =0.507..)

Enjoy