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Math Help - [SOLVED] Depend event

  1. #1
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    [SOLVED] Depend event

    hai every body... i still stuck until now for the following problem. hope somebody can guide me.

    Question
    A box contains 5 black cubes and 3 red cubes. Two cube are drawn at random from the box. find the probability that :
    (a) both cubes are black
    (b) both cubes are the same colour
    (c) both cubes are different colours

    ans given:
    5/14, 13/18 ( i also confuse this ans for which question (a)/ (b) or (c)

    My solution:
    (a) P( both cubes are black ) = P (Black,Black)
    = 5/8 * 5/8
    = 25/64

    (b) P (both cubes are the same colour) = P (Black,Black) + P (Red,Red)
    = 25/64 + 3/8*3/8
    = 25/64 + 9/64
    = 34/64
    = 17/32
    Remarks: base on my calculation it look like it wrong when i compare it with the given ans..
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  2. #2
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    remember that the second time you take a ball out there are less balls in the box i.e the first time you take a ball out the chance of it being black is 5/8 but now there are 4 black balls left and 7 balls left in total.

    sorry, cubes
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  3. #3
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    Quote Originally Posted by Tarzan View Post
    remember that the second time you take a ball out there are less balls in the box i.e the first time you take a ball out the chance of it being black is 5/8 but now there are 4 black balls left and 7 balls left in total.

    sorry, cubes
    but this question not stated with replacement or without replacement
    . is it we can consider without replacement for this case
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  4. #4
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    Quote Originally Posted by nikk View Post
    but this question not stated with replacement or without replacement
    . is it we can consider without replacement for this case

    i find if it's not stated either way the cubes generally aren't replaced, but it does depend on who wrote the question.
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  5. #5
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    Quote Originally Posted by Tarzan View Post
    i find if it's not stated either way the cubes generally aren't replaced, but it does depend on who wrote the question.
    i try to calculate it now base on your info
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  6. #6
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    Angry ans to confirm

    base on your info this is my ans:

    (a) P( both cubes are black ) = P (Black,Black)
    = 5/8 * 4/7
    = 5/14 (same as per ans)

    (b) P (both cubes are the same colour) = P (Black,Black) + P (Red,Red)
    = 5/8 * 4/7 + 3/8*2/7
    = 13/28 ( not same with ans given)

    (c) both cubes are different colours
    = P ( Black,Red) + P( Red,Black)
    = 5/8 * 3/7 + 3/8*5/7
    = 15/28 ( not same with ans given)

    any one can confirm my ans
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  7. #7
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    There is a typo in the second given answer. It should be \frac{13}{{\color{red}2}8}.
    Both the same color is: \frac{(5)(4)+(3)(2)}{(8)(7)}
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  8. #8
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    Quote Originally Posted by Plato View Post
    There is a typo in the second given answer. It should be \frac{13}{{\color{red}2}8}.
    Both the same color is: \frac{(5)(4)+(3)(2)}{(8)(7)}
    thank you both of you.....
    how about question???
    any command to my ans???
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  9. #9
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    Because answers in b & c addup 1 and answer b is correct then answer c must be also correct.
    If they are not the same color then they are different colors. Right?
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  10. #10
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    Thumbs down

    Quote Originally Posted by Plato View Post
    Because answers in b & c addup 1 and answer b is correct then answer c must be also correct.
    If they are not the same color then they are different colors. Right?
    it mean u agreed to my ans??
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  11. #11
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    Quote Originally Posted by nikk View Post
    it mean u agreed to my ans??
    Well, yes.
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