Question

A student takes an exam containing 10 multiple-choice questions. The probability of choosing a correct answer by knowledgeable guessing is 0.5. At least 6 correct answers are required to pass. If the student makes knowledgeable guesses, what is the probability that he will fail? Round your answer to four decimal places.

Answer 1

Let X be the number of correct answers he gets. Then

We need to find P(Fail) = P(Answers less than 6 correct answers)

The probability table is:

X	P(X=x)
0	0.0009766
1	0.0097656
2	0.0439453
3	0.1171875
4	0.2050781
5	0.2460938
6	0.2050781
7	0.1171875
8	0.0439453
9	0.0097656
10	0.0009766

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