This test, like many multiple-choice tests, is scored using a penalty for guessing. The test score is determined by awarding one point for each question answered correctly, deducting 0.25 points for each question answered incorrectly, and ignoring any question that is omitted. That is, the the test score is calculated using the following formula score=(1Xnumber corrected)-(0.25Xnumber incorrect)+(0 X Number omitted) (b) Suppose a student knows the correct answers for 18 questions, answers those 18 questions correctly, and chooses randomly from the 5 choices for each of the other 7 questions. Show that the expected value of the student’s score is 18 when using the the scoring formula above.
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
This test, like many multiple-choice tests, is scored using a penalty for guessing. The test score
is determined by awarding one point for each question answered correctly, deducting 0.25 points
for each question answered incorrectly, and ignoring any question that is omitted. That is, the
the test score is calculated using the following formula
score=(1Xnumber corrected)-(0.25Xnumber incorrect)+(0 X Number omitted)
(b) Suppose a student knows the correct answers for 18 questions, answers those 18
questions correctly, and chooses randomly from the 5 choices for each of the other 7
questions. Show that the
the scoring formula above.
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