SOLUTION: The probability of answering a multiple choice questions correctly by guessing is 0.25. A student guesses the answer to three multiple choice question. Find the probability that:

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Question 935781: The probability of answering a multiple choice questions correctly by guessing is 0.25. A student guesses the answer to three multiple choice question. Find the probability that:
1) at least two answers are correct.
2) less than two answers are correct.
Answer by oscargut(2103) (Show Source):
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The probability of answering a multiple choice questions correctly by guessing is 0.25.
A student guesses the answer to three multiple choice question.
Find the probability that:

1) At least two answers are correct.
2) Less than two answers are correct.

1)
Solution:
P(at least 2 answers correct) = P(2 correct)+P(3 correct)
= 3(1/4)(1/4)(3/4) + (1/4)(1/4)(1/4) = 9/64 +1/64 = 10/64 = 5/32
Answer: 5/32
2)
Solution:
P(Less 2 answers correct) = 1-P(at least 2 answers correct) = 1-5/32 = 27/32
Answer: 27/32
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