Question

Richard has just been given a 8-question multiple-choice quiz in his history class. Each question has four answers, of which only one is correct. Since Richard has not attended class recently, he doesn't know any of the answers. Assuming that Richard guesses on all eight questions, find the indicated probabilities. (Round your answers to five decimal places.)

Answer 1

Answer:

Incomplete question, but it can be answered using a binomial probability distribution, with $p = 0.25, n = 8$

Step-by-step explanation:

For each question, there are only two possible outcomes. Either he answers it correctly, or he does not. The probability of answering a question correctly is independent of any other question. Thus, the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

Richard has just been given a 8-question multiple-choice quiz in his history class.

8 questions, so $n = 8$

Each question has four answers, of which only one is correct. He guesses the answer.

This means that $p = \frac{1}{4} = 0.25$