Assume that random guesses are made for 8 multiple-choice questions on a test with 5 choices for each question, so that there are $n=8$ trials, each with probability of success (correct) given by $p=0.20$. Find the probability of no correct answers.
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The probability of no correct answers is
(Round to three decimal places as needed.)

Step 1 ：We are given a problem where random guesses are made for 8 multiple-choice questions on a test with 5 choices for each question. We are asked to find the probability of no correct answers.

Step 2 ：This is a binomial distribution problem. The binomial distribution model deals with finding the probability of success of an event which has only two possible outcomes in a series of experiments.

Step 3 ：For a random variable X if X is B(n, p) where n is the number of trials, and p is the probability of success on each trial, we can find the probability of getting exactly k successes among n trials is given by the function: $P(X=k)=C(n,k)\ast (p^k)\ast (1-p{)}^{(}n-k)$ where C(n, k) is the binomial coefficient.

Step 4 ：In this case, we are looking for the probability of no correct answers, which means k=0. So we can substitute n=8, p=0.20 and k=0 into the formula and calculate the result.

Step 5 ：Substituting the given values into the formula, we get $P(X=0)=C(8,0)\ast ({0.2}^0)\ast (1-0.2{)}^{(}8-0)$

Step 6 ：Solving the above expression, we get $P=0.1677721600000001$

Step 7 ：Rounding to three decimal places as needed, we get $P=0.168$

Step 8 ：Final Answer: The probability of no correct answers is $\boxed{{\displaystyle 0.168}}$