Answer to Question #119423 in Statistics and Probability for Nk

Question

A20. Emmanuel is given a multiple-choice exam with ten questions and each question with five possible answers. He decided to guess randomly for each question. What is the probability that he will get at least six questions correct?

Answer 1

Probability of question correct $= \frac{1}{5}$

Probability of question Incorrect $=\frac {4}{5}$

Probability get at least six questions correct

$=_{10}C_{6} (\frac{1}{5})^6(\frac {4}{5})^4 +_{10}C_{7} (\frac{1}{5})^7(\frac {4}{5})^3+_{10}C_{8} (\frac{1}{5})^8(\frac {4}{5})^2+_{10}C_{9} (\frac{1}{5})^9(\frac {4}{5})^1+_{10}C_{10} (\frac{1}{5})^{10} (\frac {4}{5})^0$

$= 6.3739 \times 10 ^{-3}$