Part 1 Probability will be the basis of all future topics, and you will find that the resulting interpretation of a probability and the conclusion that can make from a probability is more important than that calculation itself. Consider the following probabilities found for the given situations, then answer the questions that follow: Situation 1: If randomly guessing, the probability that a person can correctly guess your birthday (month and day) on the first try is 365 = 0.0027. The probability that a person can correctly guess the birthday of two people in a row is ( ) = 0.0000075. You and 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 seen 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. QUESTION: Although he did not run the mile at the 5.7 minute pace that he claimed, would you be able to take his word for it given his result OR is this result enough evidence to prove that he is lying? Explain, and use the given 0.31 probability in your explanation. Part 2 Probability is one topic that students struggle with a lot. What is one topic or question that you had or still have difficulty grasping