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 probability of landing on grey

There is 1 grey region out of 6 total regions. So the probability of landing on grey in the first spin, $P(\text{grey})=\frac{1}{6}$.

Step2: Calculate probability of landing on blue

There are 3 blue regions out of 6 total regions. So the probability of landing on blue in the second spin, $P(\text{blue})=\frac{3}{6}=\frac{1}{2}$.

Step3: Use multiplication rule for independent events

Since the two spins are independent events, the probability of landing on grey and then blue is $P = P(\text{grey})\times P(\text{blue})$.
$P=\frac{1}{6}\times\frac{1}{2}=\frac{1}{12}$.

Answer:

$\frac{1}{12}$