Question

On a multiple choice test, if you randomly guessed on three questions, then what is the probability you got at least one of them correct?

Answer 1

Number of Questions =3

Probability of giving a correct answer

`=(1)/(3)`

Probability of giving two correct answers

`=(2)/(3)`

Probability of giving all correct answers

`=(3)/(3)\\\\=1`

Probability that at least one of them is correct

`=_(1)^(3)\textrm{C}\\\\=(3!)/((3-1)! *1!)\\\\=3 \text{ways}\\\\=(1)/(3) * (1)/(3) * (1)/(3) \\\\=(1)/(27)`

Probability that two of them is correct

`=_(2)^(3)\textrm{C}\\\\=(3!)/((3-2)! *2!)\\\\=3 \text{ways}\\\\=(2)/(3) * (2)/(3) * (2)/(3) \\\\=(8)/(27)`

Probability that all of them is correct

`=_(3)^(3)\textrm{C}\\\\=(3!)/((3-3)! *3!)\\\\=1 \text{way}\\\\=1`

So, Required probability

`=(1)/(27) * (8)/(27) * 1\\\\=(8)/(729)`