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Math Help - Porbabilities

  1. #1
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    Porbabilities

    I got a homework assignement with 12 questions and I figured out 7 of them. I have no clue how to do the rest of them. On the ones I knew how to do, I used the binomial distribution and P(A|B)= P(A)(P(B|A)/P(B). Here are the problems:
    I am not looking for answers. I am looking for a formula to use for them or something. I want to be able to do them.

    1)Urn I contains two red chips and four white chips; urn II contains 3 red and one white. Ac chip is drawn at random from urn I and transfered to urn II. Then a chip is drawn from urn II.
    a) what is the prob the chip is drawn from urn II is red?
    b) Given that a red chip is drawn from urn II, what is the probability a white chip is drawn from urn I?

    2) Urn I has 3 red chip, 2 black chips, and 5 white chips; urn II has 2 red, 4 black, and 3 white chips. One chip is drawn at random from each urn. What is the probability both chips are the same color?

    3)A coin for which P(heads) = p is to be tossed twice. For what value of p will the probability of the event " same side comes up twice" be minimized.

    4) Two fair dice are rolled. What is the prob the number appearing on one will be twice the number appearing on the other?

    5) An urn contains two white chips and one red chip. One is drawn at random and replaced with an additional chip of the same color. The procedure is repeated 2 more times. Find the probabilities associated with the eight points in the sample space.
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  2. #2
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    In #1(a). Calculate P(R_2 ) = P(R_2  \cap R_1 ) + P(R_2  \cap W_1 ).
    In #1(b). Calculate P(W_1 |R_2 ) = \frac{{P(R_2  \cap W_1 )}}<br />
{{P(R_2 )}}.

    In #3, minimize the function p^2  + \left( {1 - p} \right)^2 .

    Now you respond showing work that you have done on the others.
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  3. #3
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    OKay

    I may need a little more help with Problem 1. For 1 I got:
    How do I solve for Probability of R2 union R1.
    If they were independent I would just multiply the 2 together. I don't know how to find it since they dependent. I just started this class and this is my first probability class.
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  4. #4
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    Well of course they are not independent! What happens first effects what happens second. You are adding a red or white chip to urn II.
    P(R_1  \cap R_2 ) = P(R_2 |R_1 )P(R_1 ) = \left[ {\frac{4}{5}} \right]\left[ {\frac{2}{6}} \right]
    The probability of a red first times the probability of a red second.
    Note, putting a red into urn II changes the probability of a red second.
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  5. #5
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    i tried problem 2

    For number 2, I multiplied the prb of red first by red second. then white first by white second. finally black first by black second. I got .32222. does that sound right?

    For number 4, is it just 1/12? Because there are 36 total ways you can roll 2 dice and only 3 ways of getting 2 times the one? (1,2)(2,4)(3,6)

    I figured out number 5. i just made a tree diagram. it was pretty easy once i thought about it.

    I have no idea what to do for number 3
    Last edited by PensFan10; October 22nd 2008 at 03:27 PM.
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  6. #6
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    Quote Originally Posted by PensFan10 View Post
    I multiplied the prb of red first by red second. then white first by white second. finally black first by black second.
    I got .32222. does that sound right?
    DO NOT ask me to verify numbers! I donít do that very well.
    In fact, I always required students to Ďset upí the calculation for the answer.
    Once I see the set-up, I know if the answer is correct.
    So, you need to show how you got that answer.
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