Work with others and get as much help as you like, but you must submit your own copy of your own work. Any or all problems may be graded. You must show your work for full credit, even if it only means telling us what calculator function(s) you used: providing a final answer and no work is not enough. 1. a. If you flip a coin 10 times, and it shows heads exactly 5 times, does this mean the coin must be fair? Explain. b. If you flip a coin 100 times and it shows heads exactly 50 times, does this mean the coin must be fair? Explain. c. Which case above (a or b) gives you more confidence that the coin is actually fair? d. If you flip a coin 100 times, what is the probability that the coin will show heads exactly 50 times? e. Do your responses to c. and d. above conflict with each other? Explain.