Question

1. a 6 - sided cube has a different color on each side - red, blue, green, orange, purple, and yellow. evan rolls the cube 3 times. what is the probability that he will roll purple all 3 times?

Explanation:

Step1: Probability of rolling purple once

The cube has 6 sides. The probability of rolling purple on a single roll is $\frac{1}{6}$ since there is 1 purple - side out of 6 sides.

Step2: Probability of independent events

Rolling the cube multiple times are independent events. For independent events $A$, $B$, and $C$, the probability of $A$ and $B$ and $C$ occurring is $P(A)\times P(B)\times P(C)$. Here, the probability of rolling purple on the first roll is $P_1=\frac{1}{6}$, on the second roll is $P_2 = \frac{1}{6}$, and on the third roll is $P_3=\frac{1}{6}$.

Step3: Calculate the probability of rolling purple 3 times

The probability of rolling purple all 3 times is $P = \frac{1}{6}\times\frac{1}{6}\times\frac{1}{6}=\frac{1}{216}$.

Answer:

$\frac{1}{216}$