(This is a few years late, but hopefully it will help others now.)
~A number cube has 6 sides
~It’s rolled 3 times
To get the number of possible outcomes:
6^3 = 6*6*6 = 36*6 = 216
Therefore, there are 216 possible outcomes.
A cube when rolled 3 times, the total number of possible outcomes is Option (D) 216.
The sample space of an random event is defined as the set of all possible outcomes for that given experiment. In any random event, the set of possible outcomes is defined as sample points which are mutually exclusive which means they cannot occur simultaneously .
Let S denotes the sample space of the random event for rolling a cube 3 times.
For the given problem , when a cube is rolled for once , the sample space for the random experiment of rolling a cube once is 6 .
This is because a cube has six sides and the total number of possible outcomes can be the total number of events ranging from 1 to 6 .
Also from formula of probability, the total number of possible outcomes is calculated by [tex]x^{n}[/tex]
where x is the total number of outcomes for any random event occurring for once and n is the number of times the event is occurring for the given problem.
In this problem, x = 6 and n = 3 as number of times cube rolled is 3.
Thus the sample space for the random event n(S) or the total number of possible outcomes is -
[tex]6^{3}[/tex] = [tex]216[/tex]
Therefore, when a cube when rolled 3 times, the total number of possible outcomes is Option (D) 216.
To learn more about total number of possible outcomes, refer -
https://brainly.com/question/1563396
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