Question

assume that random guesses are made for 2 multiple - choice questions on a test with 2 choices for each question, so that there are n = 2 trials, each with probability of success (correct) given by p = 0.50. find the probability of no correct answers. click on the icon to view the binomial probability table. the probability of no correct answers is . (round to three decimal places as needed.)

Explanation:

Step1: Recall binomial probability formula

The binomial probability formula is $P(X = k)=C(n,k)\times p^{k}\times(1 - p)^{n - k}$, where $n$ is the number of trials, $k$ is the number of successes, $p$ is the probability of success on a single - trial, and $C(n,k)=\frac{n!}{k!(n - k)!}$. Here, $n = 2$, $k = 0$, and $p=0.5$.

Step2: Calculate the combination $C(n,k)$

First, calculate $C(2,0)=\frac{2!}{0!(2 - 0)!}=\frac{2!}{2!}=1$.

Step3: Calculate $(1 - p)^{n - k}$

Since $p = 0.5$, then $1-p=0.5$, $n = 2$, and $k = 0$, so $(1 - p)^{n - k}=(0.5)^{2-0}=(0.5)^{2}=0.25$.

Step4: Calculate the probability

$P(X = 0)=C(2,0)\times(0.5)^{0}\times(0.5)^{2}$. Since $(0.5)^{0}=1$ and $C(2,0) = 1$, then $P(X = 0)=1\times1\times0.25 = 0.250$.

Answer:

$0.250$