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The odds are 1:8 because there is only one side that contains a 6 and all of the others contain a different number. Only 1 side out of 8 sides contains a 6 so you have a 1 in 8 chance of rolling a six, or 1:8.

Answer:

[tex]\frac{1}{7}[/tex] or 1 to 7.

Step-by-step explanation:

We are asked to find the odds against rolling a 6 on a eight​-sided die.

[tex]\text{Odds}=\frac{P}{1-P}[/tex], where p represents probability of an event.

We will find probability of getting 6 on an 8 sided die as:

[tex]\text{Probability of getting 6}=\frac{1}{8}[/tex]

[tex]\text{Odds}=\frac{\frac{1}{8}}{1-\frac{1}{8}}[/tex]

[tex]\text{Odds}=\frac{\frac{1}{8}}{\frac{8}{8}-\frac{1}{8}}[/tex]

[tex]\text{Odds}=\frac{\frac{1}{8}}{\frac{8-1}{8}}[/tex]

[tex]\text{Odds}=\frac{\frac{1}{8}}{\frac{7}{8}}[/tex]

[tex]\text{Odds}=\frac{1}{8}\times \frac{8}{7}[/tex]

[tex]\text{Odds}=\frac{1}{7}[/tex]

Therefore, the odds against rolling a 6 is 1 to 7.

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