Question

scott has a six - sided dice. the sides of the dice are displayed below:
1 2 3 4 5 6
assuming that the dice is fair. find the theoretical probability of rolling each value. write your answers as percents correct to two decimal places.
(example: 54.32%. you would type 54.32)
p(1)=□ % p(2)=□ %
p(3)=□ % p(4)=□ %
p(5)=□ % p(6)=□ %

Explanation:

Step1: Recall probability formula

For a fair six - sided die, the number of favorable outcomes for each value (e.g., rolling a 1, 2, etc.) is 1, and the total number of possible outcomes is 6. The formula for probability \(P(event)=\frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}\). So for each value \(x\) (where \(x = 1,2,\cdots,6\)), \(P(x)=\frac{1}{6}\).

Step2: Convert to percentage

To convert the fraction \(\frac{1}{6}\) to a percentage, we calculate \(\frac{1}{6}\times100\%\). \(\frac{1}{6}\approx0.1667\), and \(0.1667\times 100 = 16.67\%\) (rounded to two decimal places). Since the die is fair, the probability of rolling each value is the same.

Answer:

\(p(1)=\boldsymbol{16.67}\) %
\(p(2)=\boldsymbol{16.67}\) %
\(p(3)=\boldsymbol{16.67}\) %
\(p(4)=\boldsymbol{16.67}\) %
\(p(5)=\boldsymbol{16.67}\) %
\(p(6)=\boldsymbol{16.67}\) %