QUOTE(plouffle0789 @ Aug 9 2023, 06:20 PM)
216 Possible Outcomes: Rolling three six-sided dice gives you a total of 216 different combinations (6 sides * 6 sides * 6 sides).
"Big" Outcome: There are 35 ways to get a "big" outcome (where the total of the three dice is between 11 and 17, excluding triples).
"Small" Outcome: There are also 35 ways to get a "small" outcome (where the total of the three dice is between 4 and 10, excluding triples).
"Triple" Outcome: A "triple" occurs when all three dice show the same number. There are 6 ways this can happen.
Probabilities:
Probability of "big" = 35 big outcomes / 216 total outcomes = 35/216.
Probability of "small" = 35 small outcomes / 216 total outcomes = 35/216.
Probability of "triple" = 6 triple outcomes / 216 total outcomes = 6/216.
Using 72 as a Common Denominator:
To simplify the probabilities, you can multiply both the numerator and denominator of each fraction by a number that results in 72:
Probability of "big" = 35/72 β
0.486111
Probability of "small" = 35/72 β
0.486111
Probability of "triple" = 2/72 β
0.027778
Some error. Should be"Big" Outcome: There are 35 ways to get a "big" outcome (where the total of the three dice is between 11 and 17, excluding triples).
"Small" Outcome: There are also 35 ways to get a "small" outcome (where the total of the three dice is between 4 and 10, excluding triples).
"Triple" Outcome: A "triple" occurs when all three dice show the same number. There are 6 ways this can happen.
Probabilities:
Probability of "big" = 35 big outcomes / 216 total outcomes = 35/216.
Probability of "small" = 35 small outcomes / 216 total outcomes = 35/216.
Probability of "triple" = 6 triple outcomes / 216 total outcomes = 6/216.
Using 72 as a Common Denominator:
To simplify the probabilities, you can multiply both the numerator and denominator of each fraction by a number that results in 72:
Probability of "big" = 35/72 β
0.486111
Probability of "small" = 35/72 β
0.486111
Probability of "triple" = 2/72 β
0.027778
Probability of "big" = 105 big outcomes / 216 total outcomes = 105/216 = 35/72
Probability of "small" = 105 small outcomes / 216 total outcomes = 105/216 = 35/72
Probability of "triple" = 6 triple outcomes / 216 total outcomes = 6/216 = 2/72= 1/36
Aug 9 2023, 09:47 PM

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