Project 1 Consider the following experiment: flip a penny and a nickel, recording heads or tails for each coin, and roll a pair of fair, six-sided dice and record the sum.
Write down the sample space corresponding to this experiment as written. Does this sample space consist of equally likely outcomes? If not is there some underlying space which does have equally likely outcomes? If so what is this underlying space?
Perform this experiment 20 times. What is the average sum rolled on the pair of dice? What is the standard deviation of this sum? The median?
Using the data above what is the empirical probability of one head and a sum of at least 8? What is the empirical probability of a sum of 7 and at least one head? What is the empirical probability of a sum of 8 or 9 and two heads?
Perform the experiment 50 times. Using this new data, what is the empirical probability of one head and a sum of at least 8? What is the empirical probability of a sum of 7 and at least one head? What is the empirical probability of a sum of 8 or 9 and two heads?
What are the theoretical probabilities for each of these questions? Are the empirical and theoretical probabilities the same? Which of the two sets empirical probabilities is closest to the theoretical probability? Explain.