Question

A multiple choice test contains questions

with four options each: A, B, C, or D. If


Natalie randomly guesses on the last three


questions, what is the probability that she


gets all three correct?

Answer 1

Probability of getting all three correct answer =
`(1)/(64)`

Explanation:

Given - A multiple choice test contains questions with four options each: A, B, C, or D. If Natalie randomly guesses on the last three questions.

To find - what is the probability that she gets all three correct.

Proof -

Given that, question has 4 options.

And 1 option can be correct,

Let

x be that Natalie gives correct answer.

So,

Probability of getting, correct answer, P(x) =
`(1)/(4)`

So,

Probability of getting, incorrect answer, P(x') = 1 -
`(1)/(4)` =
`(3)/(4)`

Now,

Given that, she guess the 3 questions.

All correct means,

first, second, third question answer is correct.

So,

Probability of getting all three correct answer =
`(1)/(4)`×
`(1)/(4)`×
`(1)/(4)` =
`(1)/(64)`