Question

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

Explanation:

Step1: Determine the probability of not landing on blue in one spin

The spinner has 8 equal - sized regions. There is 1 blue region. So the number of non - blue regions is \(n = 7\).
The probability of an event \(P(E)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\).
For one spin, the probability of landing on a color other than blue, \(P(\text{not blue}_1)=\frac{7}{8}\)

Step2: Use the multiplication rule for independent events

Since the two spins are independent events (the outcome of the first spin does not affect the outcome of the second spin), and for two independent events \(A\) and \(B\), \(P(A\cap B)=P(A)\times P(B)\)
Let \(A\) be the event of not landing on blue in the first spin and \(B\) be the event of not landing on blue in the second spin.
\(P(\text{not blue}_1\cap\text{not blue}_2)=P(\text{not blue}_1)\times P(\text{not blue}_2)\)
Since \(P(\text{not blue}_1) = P(\text{not blue}_2)=\frac{7}{8}\)
\(P(\text{not blue}_1\cap\text{not blue}_2)=\frac{7}{8}\times\frac{7}{8}=\frac{49}{64}\)

Answer:

\(\frac{49}{64}\)