the fair spinner shown is spun 2 times. the set of possible outcomes are: s = {rr, bb, yy, gg, rb, br, ry…

Explanation:

Step1: Determine probability of landing on yellow in a single spin

The spinner is divided into 4 equal - colored sections. So the probability of landing on yellow in a single spin, $p=\frac{1}{4}=0.25$, and the probability of not landing on yellow in a single spin, $q = 1 - p=1 - 0.25 = 0.75$.

Step2: Use binomial probability formula

The binomial probability formula is $P(X = k)=C(n,k)\times p^{k}\times q^{n - k}$, where $n$ is the number of trials, $k$ is the number of successes, $p$ is the probability of success in a single trial, $q$ is the probability of failure in a single trial, and $C(n,k)=\frac{n!}{k!(n - k)!}$. Here, $n = 2$ (number of spins), $k = 1$ (number of times landing on yellow), $p = 0.25$, and $q = 0.75$. First, calculate $C(2,1)=\frac{2!}{1!(2 - 1)!}=\frac{2!}{1!1!}=\frac{2\times1!}{1!×1}=2$. Then, $P(X = 1)=C(2,1)\times(0.25)^{1}\times(0.75)^{2 - 1}$.

Step3: Calculate the probability

$P(X = 1)=2\times0.25\times0.75= 0.375$.

Answer:

0.375