Answer:
Incomplete question, but it can be answered using a binomial probability distribution, with [tex]p = 0.25, n = 8[/tex]
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.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
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 [tex]n = 8[/tex]
Each question has four answers, of which only one is correct. He guesses the answer.
This means that [tex]p = \frac{1}{4} = 0.25[/tex]
