(Make sure to show your work so we can assign partial credit!) Imagine a perfectly fair coin-flipping machine. You know that it's flipping either a normal coin (i.e., an evenly-weighted coin with heads on one side and tails on the other); or else a two-headed coin (i.e., a coin with heads on both sides). You can't see the coin, but the machine accurately reports the outcome of every flip it performs. (a) Suppose that the machine flips the coin once, and the outcome is heads. Does this outcome constitute evidence for or against (or neither for nor against) the hypothesis that the coin is two-headed? What is the strength factor of this evidence, with respect to the given hypothesis? (b) Suppose that the coin is flipped twice, and the outcome is heads both times. Since those events are independent, the probability that the coin comes up heads both times equals the probability that it comes up heads on the first flip multiplied by the probability that it comes up heads on the second flip. What is the strength factor of this evidence, with respect to the hypothesis that the coin is two-headed? (c) Suppose that the coin is flipped n