Question

use the spinner shown. it is equally probable that the pointer will land on any one of the eight regions. if the pointer lands on a borderline, spin again. if the pointer is spun three times, find the probability that it will land on green and then blue and then yellow. find the probability that the spinner will land on green and then blue and then yellow. (type an integer or a simplified fraction.)

Explanation:

Step1: Determine probability of green

There are 8 equal - sized regions on the spinner, and 2 are green. So the probability of landing on green, $P(G)=\frac{2}{8}=\frac{1}{4}$.

Step2: Determine probability of blue

After the first spin, there are still 8 regions. 2 are blue, so the probability of landing on blue, $P(B)=\frac{2}{8}=\frac{1}{4}$.

Step3: Determine probability of yellow

After the second spin, there are 8 regions. 2 are yellow, so the probability of landing on yellow, $P(Y)=\frac{2}{8}=\frac{1}{4}$.

Step4: Use multiplication rule for independent events

Since the spins are independent events, the probability of green then blue then yellow is $P = P(G)\times P(B)\times P(Y)$.
$P=\frac{1}{4}\times\frac{1}{4}\times\frac{1}{4}=\frac{1}{64}$.

Answer:

$\frac{1}{64}$