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Math Help - Missing steps in probability question.

  1. #1
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    Missing steps in probability question.

    Hi,

    This is my first post - Hello

    This question is quite long (but simple) so please bare with me...

    "In a multiple-choice science test Geoff does not know the answer to questions 3 and 8. He has the choice of five answers (A, B, C, D or E) for each question. For question 8 he knows for certain that answers B and E are incorrect. He must guess from the rest of the answers. For questions 3 he must guess from all five of the answers. He is equally likely to choose any of the answers.

    The correct answer to question 3 is E and for question 8 is it A. What is the probability that he gets:

    a. Both questions correct.

    b. Question 3 correct or questions 8 correct but not both correct.

    c. At least one question correct "


    I think I can answer a correctly:

    P(8 AND 3 correct) = P(1/3) * P(1/5) = 1/15

    But for b, I thought the working should be:

    P(8 OR 3 correct) = P(1/3) + P(1/5) = P(5/15) + P(3/15) = 8/15

    however the answer to b (in the book) is 2/5. Which suggests to me the book is workings is as follows:

    P(3 OR 8 correct) = P(1/5) + P(1/5) = 2/5.

    So my question is, why does the book use 1/5 as the probability of getting question 8 correct, when the statement says he knows for sure that B and E are incorrect (I guess this stems from the fact that I used the logic of 1/3 for question a)

    Any pointers would be much appreciated.

    Thanks
    Last edited by cp3o; June 17th 2011 at 01:18 PM. Reason: Correctly order questions (a,b,c i/o a,c,d)
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  2. #2
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    Re: Missing steps in probability question.

    Quote Originally Posted by cp3o View Post
    "In a multiple-choice science test Geoff does not know the answer to questions 3 and 8. He has the choice of five answers (A, B, C, D or E) for each question. For question 8 he knows for certain that answers B and E are incorrect. He must guess from the rest of the answers. For questions 3 he must guess from all five of the answers. He is equally likely to choose any of the answers.

    The correct answer to question 3 is E and for question 8 is it A. What is the probability that he gets:

    a. Both questions correct.

    c. Question 3 correct or questions 8 correct but not both correct.

    d. At least one question correct "


    I think I can answer a correctly:

    P(8 AND 3 correct) = P(1/3) * P(1/5) = 1/15

    But for b, I thought the working should be:

    P(8 OR 3 correct) = P(1/3) + P(1/5) = P(5/15) + P(3/15) = 8/15

    however the answer to b (in the book) is 2/5.
    Well I disagree with both you and the textbook.
    P(\text{8 or 3})=P(8)+P(3)-P(\text{8 and 3})=\frac{1}{3}+\frac{1}{5}-\frac{1}{15}
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  3. #3
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    Re: Missing steps in probability question.

    Quote Originally Posted by Plato View Post
    Well I disagree with both you and the textbook.
    P(\text{8 or 3})=P(8)+P(3)-P(\text{8 and 3})=\frac{1}{3}+\frac{1}{5}-\frac{1}{15}
    Thanks for the reply. Could you explain why you did it that way? I thought mutually exclusive events are P(A or B) = P(A) + P(B). Wouldn't your answer be correct for question d (at least one correct)?
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  4. #4
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    Re: Missing steps in probability question.

    Quote Originally Posted by cp3o View Post
    I thought mutually exclusive events are P(A or B) = P(A) + P(B). Wouldn't your answer be correct for question d (at least one correct)?
    First you explain why think they are mutually exclusive events.
    If they were then P(\text{8 and 3})=0.
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  5. #5
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    Re: Missing steps in probability question.

    I think they are mutually exclusive by the way the question is worded... Question 3 correct OR questions 8 correct but not both correct. So P(3 or 8)?

    Plato,

    Apologies if I am frustrating you, I am trying (although I know I can be!)
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  6. #6
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    Re: Missing steps in probability question.

    Quote Originally Posted by cp3o View Post
    I think they are mutually exclusive by the way the question is worded... Question 3 correct OR questions 8 correct but not both correct. So P(3 or 8)?
    Events are mutually exclusive, if they cannot occur at the same time.
    Can he answer both #3 & #8 correctly at the same time?
    If so then that are not mutually exclusive.

    This is a very very basic fact of probability:
    P(A\cup B)=P(A)+P(B)-P(A\cap B), where \cup\text{ means OR} and \cap\text{ means AND}.
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