The throw of an astragalus (see Section 1.4) has four possible outcomes, {1, 3, 4, 6}. When throwing four astragali, (a) How many ways are there to obtain a dog, i.e., for each astragalus to produce a...

Assignment 109689
Question: The throw of an astragalus has four possible outcomes, {1, 3, 4, 6}. When throwing four astragali,
(a) How many ways are there to obtain a Dog, i.e., for each astragalus to produce a 1?
(b) How many ways are there to obtain Venus, i.e., for each astragalus to produce a different outcome?
Answer: Astragalus can be considered as a four-sided die with possible outcomes 1, 3, 4, and 6. Astragalus is not balanced, i.e., all the sides are not equally likely. It is known that approximately 10% of the time, a modern sheep's astragalus will throw a 1 or a 6. The chances of throwing a 3 or a 4 are roughly 40% each.
Therefore, if X denotes the result from a single throw of an astragalus, the probability mass function of X can be written as:
    X = x
    P (X...