Question

assume that random guesses are made for 2 multiple - choice questions on a test with 5 choices for each question, so that there are n = 2 trials, each with probability of success (correct) given by p = 0.20. 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: Identify 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 $p=0.20$, so $1-p = 0.80$.

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

When $n = 2$ and $k = 0$, $C(2,0)=\frac{2!}{0!(2 - 0)!}=\frac{2!}{2!}=1$.

Step3: Calculate the probability

Substitute the values into the binomial - probability formula: $P(X = 0)=C(2,0)\times(0.20)^{0}\times(0.80)^{2 - 0}$. Since any non - zero number to the power of 0 is 1, $(0.20)^{0}=1$. Then $P(X = 0)=1\times1\times(0.80)^{2}=0.640$.

Answer:

$0.640$