You have 3 questions with 5 possible answers each. What is the probability of getting all answers correct?

Question

Also, what is the probability that you will get a 60% grade or higher on the test?

Answer 1

Out of 3 questions if 1 question is correct then score is 33.33%.

If 2 questions are correct score is 66.66%

If all three are correct score is 100%

 

So to get 60% or higher student has to answer at-least 2 questions correct .

P(2 questions are answered correct)=3C₂ (1/5)(1/5)(4/5)=(12/125).

P(all three questions answered correctly)=1/125.

Therefore P(Getting 60% or higher)=(12/125)+(1/125)=13/125.

 

 

Answer 2

If you are guessing on these questions, the probability of getting any one of them correct is 1 out of 5, or 1/5.

 

If you guess on each of the three questions, the probability is (1/5)³ = 1/125.

 

As for the second question, I will let some other tutor answer that. That is, after you take the test.