Imagine that you want to test whether a particular coin is biased or fair by flipping the coin four times and counting the number of times it comes up heads.

a. How many different sequences can be produced by flipping the coin four times? How many different values can X (the number of heads) take on?

b. Graph the binomial distribution for N = 4 and P = .5 so that the height of each bar represents the probability that corresponds to each value of X.

c. If the coin were to land on tails four times in a row, could you reject the null hypothesis that the coin is fair? Explain.