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?

Respuesta :

a) The probability of getting the correct answer =  [tex]\frac{1}{6}[/tex]

b)  The probability of getting a correct answer after eliminating one answer is  [tex]\frac{1}{5}[/tex]

Step-by-step 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 = [tex]\frac{1}{6}[/tex]

Hence probability of getting the correct answer =  [tex]\frac{1}{6}[/tex]

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 [tex]\frac{1}{5}[/tex]

The probability of selecting a correct answer after eliminating one answer is  [tex]\frac{1}{5}[/tex]

Step 3 :

Answer :

a) The probability that student selects  correct answer =  [tex]\frac{1}{6}[/tex]

b)  The probability that student selects correct answer after eliminating one answer is  [tex]\frac{1}{5}[/tex]