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

Explanation:

Step1: Calculate the probability of landing on grey

The spinner has 6 equal - sized regions. The number of grey regions is 1.
The probability of landing on grey, \(P(\text{grey})\), is given by the formula \(P = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). So \(P(\text{grey})=\frac{1}{6}\)

Step2: Calculate the probability of landing on purple

The number of purple regions is 2.
Using the same probability formula, \(P(\text{purple})=\frac{2}{6}=\frac{1}{3}\)

Step3: Calculate the probability of landing on grey and then purple

Since the two spins are independent events, for two independent events \(A\) and \(B\), \(P(A\cap B)=P(A)\times P(B)\)
Let \(A\) be the event of landing on grey and \(B\) be the event of landing on purple.
\(P(\text{grey and then purple})=P(\text{grey})\times P(\text{purple})\)
Substitute \(P(\text{grey})=\frac{1}{6}\) and \(P(\text{purple}) = \frac{1}{3}\) into the formula:
\(P=\frac{1}{6}\times\frac{1}{3}\)
\(P=\frac{1\times1}{6\times3}=\frac{1}{18}\)

Answer:

\(\frac{1}{18}\)