– discussion

Part 1 will have you explore how we might use probability to guide us in making decisions. Do not worry if your answer is wrong, but I do want to see your thinking!
Part 2 will help to foster classroom discussion which will lead to clarifications and sharing of best study practice. 
Be sure to respond to both parts in your initial post.
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 you 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: Two magicians claim that they can read minds. The first magician asks you to think of a number between 1 and 1,000,000. The second magician asks you to think of a number between 1 and 5. Both “magicians” correctly guess your number correctly.
Question: If both magicians are really just completely guessing, which magician has a lower chance of guessing your number correctly? Which magician (the first or second) is more impressive, and whose ability is actually enough evidence to convince you that they can read minds? 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.
Question: Although he did not run the mile at the 5.7 minute pace that he claimed, would you 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?
The phrases “or” and “and” are very important in probability. Explain what “or” and “and” mean in the context of probability. In your explanation make sure you discuss how they are different.