Question

Karma wrote a multiple choice test. The scoring system worked as follows: • gain 4 points for each correct answer • lose 1 point for each incorrect answer • 0 points for unanswered question Karma received 60 points on the test a) How does the equation 4c- i=60 describe all the different combinations of correct and incorrect answers Karma could have had to get a score of 60? b) use x and y intercept to graph this equation. c)what does each intercept mean? Are both intercepts possible? Explain d) If Karma got the same number of questions correct as incorrect, how many questions did he answer on the test?​

Answer 1

a) The equation 4c - i = 60 describes all the different combinations of correct and incorrect answers that Karma could have had to get a score of 60. Here, c represents the number of correct answers and i represents the number of incorrect answers.

b) To graph the equation 4c - i = 60, we can first find the x and y intercepts.

When c = 0 (i.e. no correct answers), we have:

4(0) - i = 60
-i = 60
i = -60

So the y-intercept is -60.

When i = 0 (i.e. no incorrect answers), we have:

4c - 0 = 60
4c = 60
c = 15

So the x-intercept is 15.

c) The y-intercept (-60) represents the score Karma would receive if he got all the questions wrong, and the x-intercept (15) represents the score he would receive if he got all the questions right. Both intercepts are possible, but it is not possible to have a negative number of correct or incorrect answers.

d) If Karma got the same number of questions correct as incorrect, then he would have answered twice as many questions as the number of correct answers. Let's call this number of correct answers "x".

Then, the number of incorrect answers would also be "x", and the total number of questions answered would be:

x (correct) + x (incorrect) = 2x

We know that Karma gained 4 points for each correct answer, so his score from correct answers would be 4x. Similarly, he lost 1 point for each incorrect answer, so his score from incorrect answers would be -1x = -x.

Since his total score was 60, we can set up the equation:

4x - x = 60

Simplifying, we get:

3x = 60

Dividing both sides by 3, we get:

x = 20

Therefore, Karma answered 40 questions on the test (20 correct and 20 incorrect).

Answer 2

Answer: In a multiple choice question there are 4 alternative answers of which 1, 2, 3, or all may be correct. A candidate decides to tick answers at random. If he is allowed upto 5 chances to answer the question, the probability that he will get the marks in the question is?

It is equally likely for 1, 2, 3, or all to be correct so probability is 1/4.

Case1 when only 1 option is correct.

Since the candidate is allowed 5 chances, probability of getting correct answer is 1.

Case2 when 2 options are correct.

Toltal ways in which 2 options can be correct is (42)

, which is 6. Out of these only 1 is correct. So probability of selecting correct answer is 1/6. Since he has 5 chances the probability of getting marks is 1−(56)5

Case3 when 3 options are correct.

Total ways in which 3 options can be correct is (43)

, which is 4. Since he has 5 chances, probability of getting correct answer is 1.

case4 when all options are correct.

Only one way in which all can be correct. Probality of getting marks is 1.

So answer should be (14×1)+14×(1−(56)5)+(14×1)+(14×1)

.

Which is indeed wrong.

A friend of mine did this question as follows.

Total options: (41)+(42)+(43)+(44)

, i.e 15. Since he has 5 chances to answer, probability would be 5/15. I know this is wrong (or not?) but beacause my textbook says answer is 1/3 I couldn’t argue.

Explanation: