Step 1

Let the probability of rolling a six is \(\displaystyle={x}\)

So the probability of rolling a three is \(\displaystyle={x}\)

the probability of rolling a one is \(\displaystyle={3}{x}\)

the probability of rolling a two is \(\displaystyle={3}{x}\)

the probability of rolling a four is \(\displaystyle={3}{x}\)

the probability of rolling a five is \(\displaystyle={5}{x}\)

Step 2

We know that the total probability is 1.

So, \(\displaystyle{x}+{x}+{3}{x}+{3}{x}+{3}{x}+{5}{x}={1}\)

Or, \(\displaystyle{16}{x}={1}\)

Or, \(\displaystyle{x}={\frac{{{1}}}{{{16}}}}\)

The probability of rolling a one is \(\displaystyle={3}{x}={3}\times{\frac{{{1}}}{{{16}}}}={\frac{{{3}}}{{{16}}}}\)

The probability of rolling a two is \(\displaystyle={3}{x}={3}\times{\frac{{{1}}}{{{16}}}}={\frac{{{3}}}{{{16}}}}\)

The probability of rolling a three is \(\displaystyle={x}={\frac{{{1}}}{{{16}}}}\)

The probability of rolling a four is \(\displaystyle={3}{x}={3}\times{\frac{{{1}}}{{{16}}}}={\frac{{{3}}}{{{16}}}}\)

The probability of rolling a five is \(\displaystyle={5}{x}={5}\times{\frac{{{1}}}{{{16}}}}={\frac{{{5}}}{{{16}}}}\)

The probability of rolling a six is \(\displaystyle={x}={\frac{{{1}}}{{{16}}}}\)

Answer:

1) \(\displaystyle{\frac{{{3}}}{{{16}}}}\)

2) \(\displaystyle{\frac{{{3}}}{{{16}}}}\)

3) \(\displaystyle{\frac{{{1}}}{{{16}}}}\)

4) \(\displaystyle{\frac{{{3}}}{{{16}}}}\)

5) \(\displaystyle{\frac{{{5}}}{{{16}}}}\)

6) \(\displaystyle{\frac{{{1}}}{{{16}}}}\)

Let the probability of rolling a six is \(\displaystyle={x}\)

So the probability of rolling a three is \(\displaystyle={x}\)

the probability of rolling a one is \(\displaystyle={3}{x}\)

the probability of rolling a two is \(\displaystyle={3}{x}\)

the probability of rolling a four is \(\displaystyle={3}{x}\)

the probability of rolling a five is \(\displaystyle={5}{x}\)

Step 2

We know that the total probability is 1.

So, \(\displaystyle{x}+{x}+{3}{x}+{3}{x}+{3}{x}+{5}{x}={1}\)

Or, \(\displaystyle{16}{x}={1}\)

Or, \(\displaystyle{x}={\frac{{{1}}}{{{16}}}}\)

The probability of rolling a one is \(\displaystyle={3}{x}={3}\times{\frac{{{1}}}{{{16}}}}={\frac{{{3}}}{{{16}}}}\)

The probability of rolling a two is \(\displaystyle={3}{x}={3}\times{\frac{{{1}}}{{{16}}}}={\frac{{{3}}}{{{16}}}}\)

The probability of rolling a three is \(\displaystyle={x}={\frac{{{1}}}{{{16}}}}\)

The probability of rolling a four is \(\displaystyle={3}{x}={3}\times{\frac{{{1}}}{{{16}}}}={\frac{{{3}}}{{{16}}}}\)

The probability of rolling a five is \(\displaystyle={5}{x}={5}\times{\frac{{{1}}}{{{16}}}}={\frac{{{5}}}{{{16}}}}\)

The probability of rolling a six is \(\displaystyle={x}={\frac{{{1}}}{{{16}}}}\)

Answer:

1) \(\displaystyle{\frac{{{3}}}{{{16}}}}\)

2) \(\displaystyle{\frac{{{3}}}{{{16}}}}\)

3) \(\displaystyle{\frac{{{1}}}{{{16}}}}\)

4) \(\displaystyle{\frac{{{3}}}{{{16}}}}\)

5) \(\displaystyle{\frac{{{5}}}{{{16}}}}\)

6) \(\displaystyle{\frac{{{1}}}{{{16}}}}\)