Question

A student is taking a quiz with nine questions. Each question has answers: A, B, C, or D. The student guesses on each question
     
      a) how many repetitions for this problem?
      b) what is the probability of success on the 1st repetition?
   c) what is the probability of guessing 3 answers correctly?

d) what is the probability of guessing at most 2 correct?

Answer 1

A student is taking a quiz with nine4 questions.

Each question has four options out of which only one is correct.

Hence, there are four possibilities for each question.

If the student guesses the answer, this situation is similar to Simple Random Sampling With Replacement (SRSWR).

a)

Hence the total n questions having m options have m^n possible repetations.

For the given question, n=9 and m=4

Therefore, total number of repetation are

b)

As the question deals with SRSWR, the probability of sucess in any repetition is same; and that is equal to receprocal of number of repetition.

Therefore, the probabiliti of sucess ion the first repetition is

c)

Now, the probabilitiy of guessing an answer correctly, is same for any other question.

For a question of 4 possible answer, the probability of guessing one answer correctly is 1/4.

Let us denote P(x) as the probability of guessing x answers correctly.

Hence, the probability of guessing 3 answers correctly is equal to,

d)

The probability of guessing at most 2 correct is given by,