Jacob rolls 4 regular dices (six sided standard). One White, One orange, One Yellow, One Purple, a) Please explain and describe what a 'state' is, and the given ensemble that represents the following situation involving Jacob. How many bits of info is missing? b) If the sum of the faces of the four dice is known to be six, what ensemble best represents the situation involving Jacob? How many bits of info are still missing? c) The total roll is 6 as shown in the below chart. What are the probabilities P, – Pg for the various faces 1-6 of the white Die? Also please calculate how much missing info is associated with this Prob distribution

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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Jacob rolls 4 regular dices (six sided standard). One White, One orange, One Yellow, One
Purple,
a) Please explain and describe what a 'state' is, and the given ensemble that represents
the following situation involving Jacob. How many bits of info is missing?
b) If the sum of the faces of the four dice is known to be six, what ensemble best
represents the situation involving Jacob? How many bits of info are still missing?
c) The total roll is 6 as shown in the below chart. What are the probabilities P, – P, for
the various faces 1-6 of the white Die? Also please calculate how much missing info
is associated with this Prob distribution
Below chart for c:
Die
Normal
ORANGE Grime
Side 1 | Side 2 | Side 3 Side 4| Side 5 | Side 6 | Mean Roll
3.5
3.5
4.
3
3
3
3.
3
6.
PURPLE Grime
YELLOW Grime
2
2
3.5
4
4
3.5
d) Please calculate a numerical value for the ratio for the answer in part c to the
answer in part b. If this ratio is not equal to one-fourth (.25), please explain why it
makes sense that the missing info associated with one out of the four dice is more
(or less) then one-fourth of the total
Transcribed Image Text:Jacob rolls 4 regular dices (six sided standard). One White, One orange, One Yellow, One Purple, a) Please explain and describe what a 'state' is, and the given ensemble that represents the following situation involving Jacob. How many bits of info is missing? b) If the sum of the faces of the four dice is known to be six, what ensemble best represents the situation involving Jacob? How many bits of info are still missing? c) The total roll is 6 as shown in the below chart. What are the probabilities P, – P, for the various faces 1-6 of the white Die? Also please calculate how much missing info is associated with this Prob distribution Below chart for c: Die Normal ORANGE Grime Side 1 | Side 2 | Side 3 Side 4| Side 5 | Side 6 | Mean Roll 3.5 3.5 4. 3 3 3 3. 3 6. PURPLE Grime YELLOW Grime 2 2 3.5 4 4 3.5 d) Please calculate a numerical value for the ratio for the answer in part c to the answer in part b. If this ratio is not equal to one-fourth (.25), please explain why it makes sense that the missing info associated with one out of the four dice is more (or less) then one-fourth of the total
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