Question

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

Answer 1

Correct Answer - C
Probability of guessing a correct answer, `p=(1)/(3)` and probability of guessing a wrong answer, `q=2//3`
`:. ` The probabiliy of guessing a 4 or more correct answers `overset(5)""C_(4)((1)/(4))^(4).(2)/(3)+overset(5)""C_(5)((1)/(3))^(5)=5.(2)/(3^(5))+(1)/(3^(5))=(11)/(3^(5))`