If randomly guessing, the probability that a person can correctly guess your birthday (month and day) on the first try is 1365=0.0027. The probability that a person can correctly guess the birthday of two people in a row is (1365)2=0.0000075. You and a friend are out one night and you meet a magician who bets that she can randomly guess both of your birthdays on the first try. QUESTION: If the magician does guess both of your birthdays, would you believe it was by pure chance, or would you believe that the magician knew your birthdays by some other means (whether that be magic, being a creepy stalker, etc.)? Explain.

Situation 2: Mark claims that his mean time for running a mile is 5.7 minutes and has a standard deviation of 0.2 minutes. This claim seems a bit fast and you want to put him to the test, so you make him run a mile. He runs the mile in 5.8 minutes, which is slower than his claim. However, if he is telling the truth, there is about a 0.31 probability, of having a time at least as high as 5.8 minutes.