a student guesses on every question of multiple choice quiz with 6 questions each with 3 possible answers. what is the probability that at least 5 of his answers are correct

P[ x >= 5 ]  = 0,005487  

Step-by-step explanation:

The possibility of the student to answer correctly one question is 1/3

We have three answers and only one is right.

The possibility of answer at least 5 right question is:

Possibility of answer 6 question plus the possibility of answer 5 questions

The possibility of answering at least 5 answers are correct is:

To answer 2 questions  1/3*1/3   =  1/9

To answer three    1/3*1/3*1/3   =  1/ 27

To answer 5   is  1/3*1/3*1/3*1/3*1/3   =  1/243

And to answer all the question right is (6) is  1/729

Therefore probability of answer at least 5 right questions is

P[ x >= 5 ]  = P [5] + P [6]

P[ x >= 5 ]  =  1/ 243  + 1/729

P[ x >= 5 ]  = 972/ 177147

P[ x >= 5 ]  = 0,005487            

step-by-step explanation: