Let the probability of rolling a six be x.
Given that the probability of rolling a three is the same as rolling a six.
The probability of rolling a three=x
Given that the probability of rolling a five is 3 times that of rolling a three.
The probability of rolling a five =3x.
Given that the probability of rolling a one, two, or four is 3 times that of a six.
The probability of rolling a one =3x.
The probability of rolling a two =3x.
The probability of rolling a four =3x.
We know that the total probability is 1.
The sum of the probability of one, two, three, four, five, and six =1
[tex]3x+3x+x+3x+3x+x=1[/tex][tex]14x=1[/tex]Dividing both sides by 14, we get
[tex]\frac{14x}{14}=\frac{1}{14}[/tex][tex]x=\frac{1}{14}[/tex]Substitute x=1/14 to get the required probabilities.
The probability of rolling a one is
[tex]3x=3\times\frac{1}{14}=\frac{3}{14}[/tex]The probability of rolling a two is
[tex]3x=3\times\frac{1}{14}=\frac{3}{14}[/tex]The probability of rolling a three is
[tex]x=\frac{1}{14}[/tex]The probability of rolling a four is
[tex]3x=3\times\frac{1}{14}=\frac{3}{14}[/tex]The probability of rolling a five is
[tex]3x=3\times\frac{1}{14}=\frac{3}{14}[/tex]The probability of rolling a six is
[tex]x=\frac{1}{14}[/tex]