We are given a number of darts. Suppose it is known that each time we throw a dart at a target, we have a probability of 1/4 of hitting the target. An experiment consists of throwing three darts at the target and observing the sequence of hits and misses (e. g., one possible outcome might be (H, M, M)).
(a) Find a probability assignment for the eight outcomes of this experiment that leads to a probability of 1/ 4 of hitting the target on any toss. Note, your assignment must satisfy the axioms of probability.
(b) Is the probability assignment you chose unique? That is, are there other possible probability assignment that lead to a probability of 1/ 4 of hitting the target on any toss, or is yours the only valid assignment? Carefully prove your answer.