A student guesses on every question of a​ multiple-choice test that has 6 ​questions, each with 3 possible answers. What is the probability that the student will get at least 4 of the questions​ right?

Answer:  The probability that the student will get at least 4 of the questions​ right is 0.0823044. Step-by-step explanation: For each question we have 3 choices. So,total choices will be : [tex]3\times3\times3\times3\times3\times3=729[/tex] Getting 4 correct means, 4 corrects and two wrongs Now, as there are 3 answer choices, out of which only one will be correct, so 2/3 is the probability if a question is answered wrong. And 1/3 is the probability if a question is answered correctly. Hence, we can consider this probability : [tex]P=(2/3)*(2/3)*(1/3)*(1/3)*(1/3)*(1/3)[/tex] = 4/729 => P = 0.00548696 We can select any combination of 2 from 6 for being wrong, so we will multiply P by (6,2)=6!/(2!*4!) = 15 So the answer is P*15 =[tex]0.00548696*15=0.0823044[/tex] The probability that the student will get at least 4 of the questions​ right is 0.0823044.