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Math Help - Balls in bags, 4 answers to 4 exam questions.

  1. #1
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    I am unsure of how to solve these questions:

    2. A bag contains 3 red balls and one blue ball. A second bag contains one red ball and one blue ball. A ball is picked out of each bag and is then placed in the other bag. What is the expected number of red balls in the first bag?

    I am not sure how to set up a tree diagram to solve this question.

    3. In an examination a candidate is given the four answers to four questions but is not told which answer applies to which question. He is asked to write down each of the four answers next to its appropriate question.

    a). Calculate in how many different ways he could write down the four answers.
    I don't even know how to do a. I thought the answer was 16 because 4*4 but the answer is actually 24.. :S How do I do this?

    b). Explain why it is impossible for him to have just 3 answer in the correct places and show that there are 6 ways of getting just two answers in the correct places.

    c). If a candidate guesses at random where the four answers are to go and X is the number of correct guesses he makes, draw up the probability distribution for X in tabular form.
    Last edited by mr fantastic; October 1st 2010 at 05:30 AM. Reason: Moved from another thread.
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  2. #2
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    Quote Originally Posted by juliak View Post
    I am unsure of how to solve these questions:

    2. A bag contains 3 red balls and one blue ball. A second bag contains one red ball and one blue ball. A ball is picked out of each bag and is then placed in the other bag. What is the expected number of red balls in the first bag?

    I am not sure how to set up a tree diagram to solve this question.

    3. In an examination a candidate is given the four answers to four questions but is not told which answer applies to which question. He is asked to write down each of the four answers next to its appropriate question.

    a). Calculate in how many different ways he could write down the four answers.
    I don't even know how to do a. I thought the answer was 16 because 4*4 but the answer is actually 24.. :S How do I do this?

    b). Explain why it is impossible for him to have just 3 answer in the correct places and show that there are 6 ways of getting just two answers in the correct places.

    c). If a candidate guesses at random where the four answers are to go and X is the number of correct guesses he makes, draw up the probability distribution for X in tabular form.
    2) The possible outcomes for bag 1 are 4R, 3R 1B and 2R 2B. Calculate the probability of each and use those probabilities to calculate the expected number of R.

    3a). Google derangement. Mr F edit: This is not relevant to the question.

    b) and c). What thoughts have you had? Where are you stuck? Part c) can be linked to a) and b) ....
    Last edited by mr fantastic; October 1st 2010 at 03:00 PM. Reason: Fixed errors pointed out below.
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  3. #3
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    I don't follow Mr. F's answer to 3a-- I think we must interpret the question differently? Anyway, according to my interpretation, the correct answer is indeed 24.

    That is because the number of possible orderings of the 4 answers is 4!.
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  4. #4
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    Quote Originally Posted by awkward View Post
    I don't follow Mr. F's answer to 3a-- I think we must interpret the question differently? Anyway, according to my interpretation, the correct answer is indeed 24.

    That is because the number of possible orderings of the 4 answers is 4!.
    Quite right. My mistake.
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  5. #5
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    Also, for Q2, don't forget that the red ball in the 2nd bag can be swopped with the blue ball in the 1st bag,
    giving 4R as the other possibility.

    For Q3 (b) Suppose he gets 3 correct. Is it possible for the 4th to then be incorrect ?
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