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 blue and then purple and then green
find the probability that the spinner will land on blue and then purple and then green.
(type an integer or a simplified fraction.)

Explanation:

Step1: Determine the probability of each spin

The spinner has 8 equal - sized regions.
The probability of landing on blue \(P(B)=\frac{3}{8}\), the probability of landing on purple \(P(P)=\frac{1}{8}\), and the probability of landing on green \(P(G)=\frac{2}{8}=\frac{1}{4}\)

Step2: Use the multiplication rule for independent events

Since the spins are independent events (the outcome of one spin does not affect the outcome of the other spins), the probability of a sequence of independent events \(A\), \(B\), and \(C\) is \(P(A\cap B\cap C)=P(A)\times P(B)\times P(C)\)
Here, \(A\) is the event of landing on blue, \(B\) is the event of landing on purple, and \(C\) is the event of landing on green
\(P = \frac{3}{8}\times\frac{1}{8}\times\frac{1}{4}\)

Step3: Calculate the product

\(P=\frac{3\times1\times1}{8\times8\times4}=\frac{3}{256}\)

Answer:

\(\frac{3}{256}\)