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Math Help - coin flip

  1. #1
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    coin flip

    A biased (weighted) coin is designed so that the probability of a head on each flip is 3/5


    If this biased coin is flipped until exactly 2 heads appear, what is the probability that it takes exactly 3 flips until the second head appears?

    I drew a tree diagram but i dont really understand what it is asking for,

    there is an answer given

    P(2H in 3 flips) = 36/125 But this doesnt make sense to me.
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  2. #2
    Senior Member pankaj's Avatar
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    It is clear that the second head must occur on the third trial.

    For the first two trials any of the following two cases are possible.
    (i)H,T
    (ii)T,H

    Let A denote the event that exactly one head occurs in first two trials
     <br />
P(A)=P(H,T)+P(T,H)=\frac{3}{5}.\frac{2}{5}+\frac{2  }{5}.\frac{3}{5}=\frac{12}{25}<br />

    Let B denote the event that head occurs on the the third trial.

     <br />
P(B)=\frac{3}{5}<br />

     <br />
P(A\cap B)=P(A)P(B)=\frac{12}{25}.\frac{3}{5}=\frac{36}{12  5}<br />

    I hope it makes sense now.
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  3. #3
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    Quote Originally Posted by brentwoodbc View Post
    A biased (weighted) coin is designed so that the probability of a head on each flip is 3/5
    This is purely a side bar.
    It has been shown by two at Cal Tech that there is no biased coin.
    Now that takes some qualifications.
    By filliping or tossing a coin, we mean that the coin is rotating is the air and it is caught on the fly (while still in the air).
    A simple thought experiment proves this. Image a coin spinning is air. Stop it.
    There is an equal chance that it ends ups on either side regardless of weight.

    I first heard of this in a lecture by a prominent author of a widely used textbook on probability and statistics. Her comment was: “the ink was dry on my new edition containing many ‘bias coin problems’ when this result hit the press”.
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  4. #4
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    thats good thank you.
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  5. #5
    Senior Member pankaj's Avatar
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    Quote Originally Posted by Plato View Post
    This is purely a side bar.
    It has been shown by two at Cal Tech that there is no biased coin.
    Now that takes some qualifications.
    By filliping or tossing a coin, we mean that the coin is rotating is the air and it is caught on the fly (while still in the air).
    A simple thought experiment proves this. Image a coin spinning is air. Stop it.
    There is an equal chance that it ends ups on either side regardless of weight.

    I first heard of this in a lecture by a prominent author of a widely used textbook on probability and statistics. Her comment was: “the ink was dry on my new edition containing many ‘bias coin problems’ when this result hit the press”.
    Can we have a biased dice
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  6. #6
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    Quote Originally Posted by Plato View Post
    This is purely a side bar.
    It has been shown by two at Cal Tech that there is no biased coin.
    Now that takes some qualifications.
    By filliping or tossing a coin, we mean that the coin is rotating is the air and it is caught on the fly (while still in the air).
    A simple thought experiment proves this. Image a coin spinning is air. Stop it.
    There is an equal chance that it ends ups on either side regardless of weight.

    I first heard of this in a lecture by a prominent author of a widely used textbook on probability and statistics. Her comment was: “the ink was dry on my new edition containing many ‘bias coin problems’ when this result hit the press”.
    ya I guess its like if you have a 10 pound ball with a volume of .5metres and a 1 pound ball with an equal volume they fall at an equal speed, but they heavy end of things does tend to fall first
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