Two people with the same birthday

Discrete Mathematics Level pending

You and a friend are standing outside a room containing 25 people, all of whom are strangers to both of you. He says, "I will give you $20 if there are not two people in that room who share a birthday (month and day). Otherwise, if there are, you pay me $20."

Do you take that bet? (In other words, is there a greater than or less than 50% probability that two people in the room share a birthday?)

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