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Math Help - coin probability

  1. #1
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    coin probability

    1. A coin is biased so that the probability that is shows heads on any one throw is p. The coin is thrown twice.

    The probability that the coin shows heads exactly once is (8/25).

    Show that 25p^2 - 25p + 4 = 0.

    2. http://img220.imageshack.us/img220/4699/fofxir0.png

    This diagram shows part of the graph of y = f(x).

    (a) Find f(3).
    (b) Solve f(x) = 6.
    (c) Find ff(1).
    (d) Find an estimate for the gradient of the curve at the point where x = -1.
    (e) The equation f(x) = k, where k is a number, has 3 solutions between x = -2 and x = 4.

    Complete the inequalities which k must satisfy.

    ..... < k < .....
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  2. #2
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    Quote Originally Posted by Jehan View Post
    1. A coin is biased so that the probability that is shows heads on any one throw is p. The coin is thrown twice.

    The probability that the coin shows heads exactly once is (8/25).

    Show that 25p^2 - 25p + 4 = 0.

    [snip]
    I have time for just one.

    The coin toss sequence was either TH or HT. The probability of each is the same and is equal to p(1 - p).

    So 2p(1-p) = \frac{8}{25} ......

    I hope the probability is equal to 1 that you can deal with it from here.
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  3. #3
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    That's awesome! Thanks.

    Now, if only someone can help me with the second question.
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  4. #4
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    I've also got another question that I can't do. D:



    (a) Find the vector OB as a column vector.

    X is the point on OB such that OX = kOB, where 0 < k < 1.

    (b) Find, in terms of k, the vectors:
    {i} OX
    {ii} AX
    {iii} XC

    (c) Find the value of k for which AX = XC.

    (d) Use your answer to part (c) to show that the diagonals of the parallelogram OABC bisect one another.
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  5. #5
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    (a) The ratio of the areas of two similar triangles is 1:k.
    Write down, in terms of k, the ratio of the lengths of their corresponding sides.

    (b)

    AB = 10cm.
    PQ is parallel to BC.

    The area of triangle APQ is half the area of triangle ABC.

    Calculate the length of AP.
    Give your answer to 2 significant figures.
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  6. #6
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    I think I've worked out part (a). Is it 1:root(k)?
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