The probability that you will guess the first answer correctly = 1/2 = 0.5 The probability that you will guess the second answer correctly = 1/2 = 0.5 The probability that you will guess the third answer correctly = 1/2 = 0.5
The probability that you will guess all three answers correctly is
(0.5) x (0.5) x (0.5) = 0.125 = 12.5% .
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Here are all the ways your answer sheet could wind up: (R = a right answer. W = a wrong answer.)
W W W W W R W R W W R R R W W R W R R R W R R R
Number of possible ways to score 0 right out of 3 questions: 1 way Number of possible ways to score 1 right out of 3 questions: 3 ways Number of possible ways to score 2 right out of 3 questions: 3 ways Number of possible ways to score 3 right out of 3 questions: 1 way
Statistically, if your answers are all pure guesses, then on the average, the score you expect is
