Answer:
[tex]P(Not\ Star) =\frac{2}{3}[/tex]
Step-by-step explanation:
Given
See attachment
Required
Theoretical probability that a roll will not land on a star
From the attachment, we have:
[tex]n = 12[/tex] --- Total space
[tex]Star = 4[/tex]
So, the theoretical probability that a roll will land on a star is:
[tex]P(Star) = \frac{n(Star)}{n}[/tex]
[tex]P(Star) = \frac{4}{12}[/tex]
[tex]P(Star) = \frac{1}{3}[/tex]
Using the complement rule, the probability that it will not land on a star is:
[tex]P(Not\ Star) = 1 - P(Star)[/tex]
[tex]P(Not\ Star) = 1 - \frac{1}{3}[/tex]
Take LCM
[tex]P(Not\ Star) =\frac{3-1}{3}[/tex]
[tex]P(Not\ Star) =\frac{2}{3}[/tex]
