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 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)

Explanation:

Step1: Count total regions and non - brown regions

The spinner has \(8\) regions in total. The number of non - brown regions is \(6\).

Step2: Calculate probability for one spin

The probability of landing on a non - brown region in one spin is \(P(\text{non - brown})=\frac{\text{Number of non - brown regions}}{\text{Total number of regions}}=\frac{6}{8}=\frac{3}{4}\).

Step3: Use the multiplication rule for independent events

Since the two spins are independent events, the probability that it lands on a non - brown region for each spin is \(P = P(\text{non - brown})\times P(\text{non - brown})\). Substitute \(P(\text{non - brown})=\frac{3}{4}\) into the formula: \(P=\frac{3}{4}\times\frac{3}{4}\).

Step4: Calculate the product

\(\frac{3}{4}\times\frac{3}{4}=\frac{3\times3}{4\times4}=\frac{9}{16}\).

Answer:

\(\frac{9}{16}\)