SOLUTION: 3. A test consists of 5 questions, and to pass the test a student has to answer at least 4 questions correctly. Each question has three possible answers, of which only one is cor

Algebra ->  Probability-and-statistics -> SOLUTION: 3. A test consists of 5 questions, and to pass the test a student has to answer at least 4 questions correctly. Each question has three possible answers, of which only one is cor      Log On


   

Question 346653: 3. A test consists of 5 questions, and to pass the test a student has to answer at least 4 questions correctly. Each question has three possible answers, of which only one is correct. If a student guesses on each question, what is the probability that the student will pass the test?
Answer by jrfrunner(365) About Me  (Show Source):
You can put this solution on YOUR website!
given
n=5, p=1/3 (prob of guessing correctly at a question)
--
let x=number of questions answered correctly
passing means x>=4 this is a binomial dist problem
==
P(x>=4)=P(x=4)+P(x=5)=C%285%2C4%29%281%2F3%29%5E4%282%2F3%29%2BC%285%2C5%29%281%2F3%29%5E5
=5%2A2%2F%283%29%5E5%2B1%2F%283%29%5E5=11/3^5=0.045