Question

It is Marcie's first turn to roll. Which ratio shows the theoretical probability that she will not land on a star space? 1/6 1/3 1/2 2/3

Answer 1

Answer:

$P(Not\ Star) =\frac{2}{3}$

Step-by-step explanation:

Given

See attachment

Required

Theoretical probability that a roll will not land on a star

From the attachment, we have:

$n = 12$ --- Total space

$Star = 4$

So, the theoretical probability that a roll will land on a star is:

$P(Star) = \frac{n(Star)}{n}$

$P(Star) = \frac{4}{12}$

$P(Star) = \frac{1}{3}$

Using the complement rule, the probability that it will not land on a star is:

$P(Not\ Star) = 1 - P(Star)$

$P(Not\ Star) = 1 - \frac{1}{3}$

Take LCM

$P(Not\ Star) =\frac{3-1}{3}$

$P(Not\ Star) =\frac{2}{3}$