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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

1 Answer

5 votes

Answer:

P[ x >= 5 ] = 0,005487

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

User Lucas Grugru
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