Question

Sally is completely unprepared for a three-question multiple-choice pop quiz, so she randomly guesses the answer to each question. If each question has four choices, then what is the probability that she gets all three questions correct?

A) 0.02

B) 0.25

C) 0.42

D) 0.75

Answer 1

Option A) 0.02

Explanation:

The probability p that one of the questions is correct is

`P = (1)/(4)`

The number of questions that will answer (number of trials) is
`n = 3`.

We want to find out the probability that
`x = 3` three questions will be answered correctly.

To calculate this probability we use the binomial formula:

`P(x) = (n!)/(x!(n-x)!) p^x(1-p)^(n-x)`

Where

`x=3\\n=3\\p=0.25`

Then:

`P(x=3) = (3!)/(3!(3-3)!) 0.25^3(1-0.25)^(3-3)`

`P(3) =0.25^3`

`P(3) = 0.0156`

P(3) = 0.0156≈0.02