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

Answer

Explanation:

Step1: Count total and non - brown regions

The spinner has 8 regions in total. There are 2 brown regions, so the number of non - brown regions is $8 - 2=6$.

Step2: Calculate probability of non - brown on one spin

The probability of landing on a non - brown region on one spin is the number of non - brown regions divided by the total number of regions. So the probability $P_1=\frac{6}{8}=\frac{3}{4}$.

Step3: Calculate probability of non - brown on two independent spins

Since the two spins are independent events, the probability of landing on a non - brown region on both spins is the product of the probabilities of landing on a non - brown region on each individual spin. So $P = P_1\times P_1=\frac{3}{4}\times\frac{3}{4}=\frac{9}{16}$.

Answer:

$\frac{9}{16}$