Question

State the number of friends (or connections) that you have on Facebook (or Linkedin). In case you have more than 365 friends or connections, think of an alternative, smaller group of friends or relatives. What is the chance that there are at least 2 people among your friends (or connections) with the same birthday (same day, not same year)? Let's find out. Please respond with an estimate of the probability that this will happen. This estimate can be intuitive or you can do some calculations: both ways are ok. In case you know the birthdays of your friends (or connections), check if your estimate of the probability corresponds to the reality.

A street performer approaches you to make a bet. He shows you three cards: one that is blue on both sides, one that is orange on both sides, and one that is blue on one side and orange on the other. He puts the cards in the bag, pulls out one, and puts it on the table. Both of you can see that the card is blue on top, but haven't seen the other side. The street performer bets you $50 that the other side of the card is also blue. Should you take the bet and WHY?

Now that the previous two questions have gotten you thinking about probability, how does probability apply to your (desired) profession?

Please note that it is extremely important that you answer the above questions by yourself, without consulting your classmates. If I notice any similarity of postings, none of the students involved will get any credit!

Answer 1