SOLUTION: Jane is taking a 10 questions multiple choice but he has not studied. Each question has 4 possible responses only one of which is correct the probability of getting each question c

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Question 985032: Jane is taking a 10 questions multiple choice but he has not studied. Each question has 4 possible responses only one of which is correct the probability of getting each question correct is 0.25. Find the probability of getting the result below if she answers all questions randomly
A) exactly 6 questions correct
B) 4 or fewer questions correct
C) 8 or more questions correct
Answer by reviewermath(1029) About Me  (Show Source):
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Jane is taking a 10 questions multiple choice but he has not studied. Each question has 4 possible responses only one of which is correct the probability of getting each question correct is 0.25. Find the probability of getting the result below if she answers all questions randomly
Let X = number of correct answers
X~Binomial(n = 10, p=0.25)
A) exactly 6 questions correct
P(X = 6) = %28matrix%282%2C1%2C10%2C6%29%29%280.25%5E6%29%280.75%5E4%29 = highlight%280.0162%29
B) 4 or fewer questions correct
P(X ≤ 4) = sum%28%28matrix%282%2C1%2C10%2Cx%29%29%280.25%5Ex%29%280.75%5E%2810-x%29%29%2Cx=0%2C4%29 = highlight%280.9219%29
C) 8 or more questions correct
P(X ≥ 8) = sum%28%28matrix%282%2C1%2C10%2Cx%29%29%280.25%5Ex%29%280.75%5E%2810-x%29%29%2Cx=8%2C10%29 = highlight%280.0004%29