Question

A​ multiple-choice test has six possible answers for each question.

​(a) If a student guesses at the​ answer, what is the probability that he or she selects the correct answer for one particular​ question?
​(​b) If the student first eliminates one of the six possible answers and guesses from the remaining​ possibilities, what is the probability that he or she selects the correct answer to that​ question?

Answer 1

a) The probability of getting the correct answer =
`(1)/(6)`

b) The probability of getting a correct answer after eliminating one answer is
`(1)/(5)`

Explanation:

Step 1 :

Number of possible answers available for each question = 6

a)

The student takes a guess at the answer, we need to obtain the probability of selecting the correct answer.

This can be obtained by dividing the favorable outcomes by the total available outcomes =
`(1)/(6)`

Hence probability of getting the correct answer =
`(1)/(6)`

Step 2 :

b)

The student eliminates one of the six possible answers. Hence the total possible answers available here is 6 - 1 = 5

The probability that the student guesses the correct answer from the available 5 answers is
`(1)/(5)`

The probability of selecting a correct answer after eliminating one answer is
`(1)/(5)`

Step 3 :

Answer :

a) The probability that student selects correct answer =
`(1)/(6)`

b) The probability that student selects correct answer after eliminating one answer is
`(1)/(5)`