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Thread: Two Different Spinners

  1. #1
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    Two Different Spinners

    # 1
    A three sided spinner is numbered 3, 4, 5. A five sided spinner is numbered 3, 3, 4, 6, 6. Both are spun at the same time. Draw a sample space and find the probability that:

    a) the sum of the scores is a prime number.
    b) the product of the scores is greater than 16.
    c) the difference in the score was exactly 1.

    -----------------------------------------------------------------

    # 2
    A bad contains three red balls, 5 yellow balls, and 2 green balls.
    A ball is selected at random, the color noted then it is put back into the bag.
    A second ball is then selected at random from the bag.

    a) A third ball is selected. Find the probability all three balls selected are yellow.

    ---------------------------------------

    my attempt for # 1

    S = {(3,3),(3,3),(3,4),(3,6),(3,6),(4,3),(4,3),(4,4),( 4,6),(4,6),(5,3),(5,3),(5,4),(5,6),(5,6)}

    prime sum = (3,4),(4,3),(4,3),(5,6),(5,6) ...........probability = (1/3)(1/5) + (1/3)(2/5) + (1/3)(2/5) + (1/3)(2/5) + (1/3)(2/5)


    ---------------------------------------------

    for # 2

    probability = (5/10)(5/10)(4/9)

    ----------------------

    Can you tell me why my answers not correct???
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  2. #2
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    Re: Two Different Spinners

    Quote Originally Posted by joshuaa View Post
    # 1
    A three sided spinner is numbered 3, 4, 5. A five sided spinner is numbered 3, 3, 4, 6, 6. Both are spun at the same time. Draw a sample space and find the probability that:

    a) the sum of the scores is a prime number.
    b) the product of the scores is greater than 16.
    c) the difference in the score was exactly 1.

    -----------------------------------------------------------------

    # 2
    A bad contains three red balls, 5 yellow balls, and 2 green balls.
    A ball is selected at random, the color noted then it is put back into the bag.
    A second ball is then selected at random from the bag.

    a) A third ball is selected. Find the probability all three balls selected are yellow.

    ---------------------------------------

    my attempt for # 1

    S = {(3,3),(3,3),(3,4),(3,6),(3,6),(4,3),(4,3),(4,4),( 4,6),(4,6),(5,3),(5,3),(5,4),(5,6),(5,6)}

    prime sum = (3,4),(4,3),(4,3),(5,6),(5,6) ...........probability = (1/3)(1/5) + (1/3)(2/5) + (1/3)(2/5) + (1/3)(2/5) + (1/3)(2/5)


    ---------------------------------------------

    for # 2

    probability = (5/10)(5/10)(4/9)

    ----------------------

    Can you tell me why my answers not correct???
    Because I have absolutely no idea what a three sided spinner is, I cannot help.

    In #2 you say the first is with replacement, but you do not say for the second ball.
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  3. #3
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    Re: Two Different Spinners

    Hey Plato.

    for # 2, the Question was asked Like that!
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  4. #4
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    Re: Two Different Spinners

    Quote Originally Posted by joshuaa View Post
    # 2
    A bad contains three red balls, 5 yellow balls, and 2 green balls.
    A ball is selected at random, the color noted then it is put back into the bag.
    A second ball is then selected at random from the bag.
    a) A third ball is selected. Find the probability all three balls selected are yellow.
    Quote Originally Posted by joshuaa View Post
    for # 2, the Question was asked Like that!
    If you say so, we must assume that the first ball is returned to the bag BUT the second ball is not returned.
    So what is the probability that all three are yellow? i.e. $\mathscr{P}(Y_1,Y_2,Y_3)=\left(\dfrac{5}{10}\cdot \dfrac{5}{10}\cdot\dfrac{4}{9}\right)$
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  5. #5
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    Re: Two Different Spinners

    I don't know why the book answer is 1/4 for # 2

    and for # 1, the answer is 4/15, but when I do calculations, I get different answer!
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  6. #6
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    Re: Two Different Spinners

    For #1 (a), here are the outcomes that yield a prime number:
    Spinner 1: Spinner 2
    3 : 4
    4 : 3 (2 outcomes yield this result)
    5 : 6 (2 outcomes yield this result)
    So, there are 5 outcomes that yield prime sums. There are a total of 15 possible outcomes. So, the probability is 5/15, not 4/15.
    (b) Outcomes that yield products greater than 16:
    3 : 6 (2 outcomes)
    4 : 6 (2 outcomes)
    5 : 4
    5 : 6 (2 outcomes)
    That is 7/15 outcomes that yield products greater than 16.
    (c) Difference in score is exactly 1:
    3 : 4
    4 : 3 (2 outcomes)
    5 : 4
    5 : 6 (2 outcomes)
    So, 6 / 15 outcomes show numbers where the difference in score is exactly 1.

    2) Your answer is correct. The book's answer is wrong. They answered a different problem than what they wrote. They answered the problem: Assume the first ball chosen is yellow and then replaced. Then another two balls are chosen at random with replacement. What is the probability all three balls chosen were yellow.
    Last edited by SlipEternal; Nov 9th 2017 at 09:30 AM.
    Thanks from joshuaa
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  7. #7
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    Re: Two Different Spinners

    Quote Originally Posted by romsek View Post
    You multiplied the probabilities instead of adding them.
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  8. #8
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    Re: Two Different Spinners

    Quote Originally Posted by SlipEternal View Post
    You multiplied the probabilities instead of adding them.
    god i give up...

    gonna take a break from this I think.
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  9. #9
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    Re: Two Different Spinners

    Quote Originally Posted by romsek View Post
    god i give up...

    gonna take a break from this I think.
    See my post (#6)
    Thanks from joshuaa
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  10. #10
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    Re: Two Different Spinners

    thanks guys. that was very helpful!
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