Amathematics competition uses the following scoring procedure to discourage students from guessing (choosing an answer randomly) on the multiple choice questions. for each correct response the score is 7 for each question left unanswered the score is 2 for each incorrect response the score is 0 if there are 5 choices for each question what is the minimum number for choices that the student must eliminate before it is advantageous to guess among the rest

To make guessing advantageous, you want the average value of each question to be greater than 2 (since leaving is blank gives 2 points)

let's go through 1 by 1:
eliminate 0: 4/5 chance of getting it wrong (0) and 1/5 chance of getting it right (7), so on average you get (4/5*0 + 1/5 *7) = 7/5 points per question

eliminate 1: 3/4 chance of getting it wrong (0) and 1/4 chance of getting it right (7), so on average you get (3/4*0 + 1/4 *7) = 7/4 points per question

eliminate 2: 2/3 chance of getting it wrong (0) and 1/3 chance of getting it right (7), so on average you get (2/3*0 + 1/3 *7) = 7/3 points per question, which is greater than 2
->the student must eliminate 2 choices before guessing is advantageous

Some continental divides span multiple continents. for example, the continental divide of americas separates the water that run through pacific ocean from the water that runs towards the atlantic and arctic oceans and the gulf of mexico.

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