The I Ching is an ancient Chinese system of asking for advice. In one version, three pennies are flipped, and if the number of heads is odd (1 or 3), a "broken line" is recorded, while if it is even (0 or 2), a "solid line" is recorded. This process is repeated six times, and then the results are used to identify one of the 26 = 64 possible patterns of solid and broken lines and corresponding advice. Assume that the coins are fair and the flips are independent. Define B to be the number of broken lines out of the six.
a. For each of the six lines, what is the probability that it is a broken line?
b. What are the possible values for B?
c. What is the probability that B = 0, so that all of the lines are solid?
d. Find the sampling distribution for B.