Marrying your sister.

[sasguru]

Not in the same year. (unless it's people in a womb, not people in a room).

chances of 2 people having same birthday: 1/365
Number of combinations of 2 people in a set of 23 people: 22+21+20...+3+2+1 = 253.
So chance of at least one of those combinations having same birthday = 253/365 = 69%

Nice attempt but your maths is wrong. As an exercise you can find out why.
Probability is interesting because it's so counter-intuitive.

[EqualOpportunities]

No matter how you write it, it's still spellt i. n. c. e. s. t.

Yes, but it is the game the whole family can play... A bit like The Wheel of Fortune.

[OwlHoot]

Probability is interesting because it's so counter-intuitive.

Yup, for example it's possible to have three non-transitive dice such that if player 1 picks any one then player 2 can pick one of the others and has a greater probability of winning.

Also (snigger), suppose a game show host tells you there's a gold bar behind one of three closed doors and asks you to choose a door (without opening it). The host then opens one of the other doors, revealing no gold bar behind it, and offers to let you change your choice to the third door. Should you switch?

[BrilloPad]

Also (snigger), suppose a game show host tells you there's a gold bar behind one of three closed doors and asks you to choose a door (without opening it). The host then opens one of the other doors, revealing no gold bar behind it, and offers to let you change your choice to the third door. Should you switch?

Easier to imagine 1000000 closed doors and 999998 doors are revealed with no gold bar being revealed.