Answer to Question #162647 in Statistics and Probability for Sunny

Question

A student randomly guesses the answers to a 6 question MCQ with three alternatives. if there is one in three chance of guessing correctly on each question, what is the probability that the student misses no questions What is the probability he misses one question?

Answer 1

Here we have 6 questions and P(correct) = 1/3

Therefore the probability that the student misses no questions is $(\frac{1}{3})^6=\frac{1}{729}=0.0014$

The probability he misses 1 question: he guesses 5 questions and misses 1

$(\frac{1}{3})^5\cdot\frac{2}{3}=\frac{2}{729}=0.0027$