A multiple-choice test has 27 questions. Each question has 5 possible answers, of which only one is correct. What is the probability that sheer guesswork will yield exactly 18 correct answers?

Around 0% probability that sheer guesswork will yield exactly 18 correct answers

Step-by-step explanation:

For each question, there are only two possible outcomes. Either you guess the correct answer, or you do not. The probability of guessing the correct answer is a question is independent of other questions. So we use the binomial probability distribution 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.

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

And p is the probability of X happening.

A multiple-choice test has 27 questions.

This means that

Each question has 5 possible answers, of which only one is correct.

This means that

What is the probability that sheer guesswork will yield exactly 18 correct answers?

This is P(X = 18).

Around 0% probability that sheer guesswork will yield exactly 18 correct answers

f(x) = - 2/3x + 5; f(5/2)

substitute 5/2 in for x:

f(5/2) = -2/3(5/2) + 5

simplify the right side:

f(5/2) = -5/3 + 5

f(5/2) = 10/3

answer:

f(5/2) = 10/3

i hope this you!