Question 172469This question is from textbook a survey of mathematics with applications
: a 10 question multiple choice exam is given, and each questions has 5 possible answers. Pascal Gonyo takes this exam and guesses at every question. use the binomial probability formula to determine the probability (to 5 decimal places) that
a. he gets exactly 2 questions correct
b. he gets no questions correct
c. he gets at least one question correct ( use information from part b)to answer this part
d. he gets at least 9 questions correct
e. without using the binomial probability formula, determine the probability that he gets exactly 2 questions correct
f. compare your answers to parts a and e. if they are not the same exaplain why
This question is from textbook a survey of mathematics with applications
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! a 10 question multiple choice exam is given, and each questions has 5 possible answers. Pascal Gonyo takes this exam and guesses at every question. use the binomial probability formula to determine the probability (to 5 decimal places) that
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All the problems are binomial with p = 1/2 and q = 1/2
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a. he gets exactly 2 questions correct
Ans: 10C2 (1/2)^10 = 45/2^10
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b. he gets no questions correct
Ans: q^10 = 1/2^10
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c. he gets at least one question correct ( use information from part b)to answer this part
Ans: 1 - p(no correct answers) = 1 - (1/2)^10
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d. he gets at least 9 questions correct
Ans 10C9*(1/2)^10 - (1/2)^10 = 10(1/2)^10 - (1/2)^10 = 9*(1/2)^10
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e. without using the binomial probability formula, determine the probability that he gets exactly 2 questions correct
Ans: 10C2(1/2)^10
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f. compare your answers to parts a and e. if they are not the same exaplain why
Ans: OK
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Cheers,
Stan H.
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