use the spinner shown. it is equally probable that the pointer will land on any one of the regions. if the…

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 green for each spin. find the probability that the spinner will land on a color other than green for each spin. (type an integer or a simplified fraction.)

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 green for each spin. find the probability that the spinner will land on a color other than green for each spin. (type an integer or a simplified fraction.)

Answer

Explanation:

Step1: Calculate single - spin non - green probability

The spinner has 8 equal regions, 2 of which are green. So the number of non - green regions is $8 - 2=6$. The probability of landing on a non - green color in a single spin is $P(\text{non - green})=\frac{6}{8}=\frac{3}{4}$.

Step2: Calculate double - spin non - green probability

Since the two spins are independent events, the probability of landing on a non - green color in both spins is the product of the probabilities of landing on a non - green color in each individual spin. Using the formula for independent events $P(A\cap B)=P(A)\times P(B)$, we have $P(\text{non - green in both spins})=\frac{3}{4}\times\frac{3}{4}=\frac{9}{16}$.

Answer:

$\frac{9}{16}$