Question

In an exam, there are 10 multiple select questions. In each multiple select question (more than one option could be correct) if a student chooses all the correct options then he/she gets
4 marks for that question, else he/she will not get any marks for the question. What is the probability that he/she will score at least
16 marks in the exam? Enter the answer up to 4 decimals accuracy.​

Answer 1

Step-by-step explanation:

Answer

Exam consists of 10 multiple choice questions.Whre out of 4 option one is correct and 3 are wrong.

Candidate get 3 marks fot every right question and −1 mark for every incorrect answer.

If the candidate attempts all of 10 questions, then from the set 15,16,17,18,19,20,.he can only achieve the score of 18, by marking 7 coorect options and 3 incorrect option.

If he attempts any more or less than 7 questions, then the score becomes out of the range of the set. Only if he does 7 correct questions, he can score 18 out of given set.

Now we know to get a score of 18, the candidate needs to correct only 7 questions out of 10, it means he will mark 3 questions incorrectly.

So number of possible combinations to get a score of 18 consists the number of ways he can chose the 7 correct answer multiplied by number of way he can incorrect the 3 questions.

Hence number of possible distinct combinations will be 10

C

7

.(3)

3

Where (3)

3

are the number of possible way he can incorrectly mark the 3 questions, as every question has 3 incorrect choice out of 4. So for 3 questions, it will 3.3.3=(3)

3

Hence total number of distinct possible combinations will be 10

C

7

.(3)

3

=120×27=3240

So correct answer is C.