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

The probability formula for an event $E$ is $P(E)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. For a fair six - sided die, the total number of outcomes when rolling the die is $n = 6$.

Step2: Calculate probability for each value

For rolling a 1, the number of favorable outcomes is 1. So $P(1)=\frac{1}{6}$. To convert to a percentage, we use the formula $P = \frac{1}{6}\times100\%$.
$P(1)=\frac{1}{6}\times100\%\approx16.67\%$.
Since the die is fair, the probability of rolling each of the numbers 2, 3, 4, 5, and 6 is also $\frac{1}{6}$ because for each number, the number of favorable outcomes is 1.
$P(2)=\frac{1}{6}\times100\%\approx16.67\%$
$P(3)=\frac{1}{6}\times100\%\approx16.67\%$
$P(4)=\frac{1}{6}\times100\%\approx16.67\%$
$P(5)=\frac{1}{6}\times100\%\approx16.67\%$
$P(6)=\frac{1}{6}\times100\%\approx16.67\%$

Answer:

$p(1)=16.67$
$p(2)=16.67$
$p(3)=16.67$
$p(4)=16.67$
$p(5)=16.67$
$p(6)=16.67$