A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get 4 or more correct answers just by guessing is (1) `(13)/(3^5)` (2) `(11)/(3^5)` (3) `(10)/(3^5)` (4) `(17)/(3^5)`

Options

A. `(17)/(3^(5))`
B. `(13)/(3^(5))`
C. `(11)/(3^(5))`
D. `(10)/(3^(5))`

Answer

C

Explanation

Answer for any question can be guessed in 3 ways. `therefore` Probability that any question is correct `=1/3`
From five questions if at least four questions are correctly answered then required probability
= Probability that four questins are correctly answered
+ Probability that five questions are correctly answered
`=""^(5)C_(4)((1)/(3))^(4)((2)/(3))+""^(5)C_(5)((1)/(3))^(5)=(11)/(3^(5))`