Question

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

Explanation:

Step1: Calculate the probability of landing on grey

There are 6 regions in total and 1 grey region. So the probability of landing on grey, \(P(\text{grey})\), is \(\frac{1}{6}\).

Step2: Calculate the probability of landing on blue

Since the spinner is spun again (independent event), there are 6 regions and 3 blue regions. So the probability of landing on blue, \(P(\text{blue})\), is \(\frac{3}{6}=\frac{1}{2}\).

Step3: Use the multiplication rule for independent events

For two independent events \(A\) and \(B\), \(P(A\cap B)=P(A)\times P(B)\). Here \(A\) is landing on grey and \(B\) is landing on blue. So \(P(\text{grey and then blue})=\frac{1}{6}\times\frac{1}{2}\).

$$ \frac{1}{6}\times\frac{1}{2}=\frac{1\times1}{6\times 2}=\frac{1}{12} $$

Answer:

\(\frac{1}{12}\)