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Math Help - [SOLVED] Binomial Probability

  1. #1
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    [SOLVED] Binomial Probability

    Hi,

    I am having trouble with the following question:

    During winter it rains on average 18 out of 30 days. Five winter days are selected at random. Find (4 d.p) the probability that:

    (a) the first two days chosen will be fine and the remainder wet
    My approach is this is an ordered selection:

    I have defined p = it will rain = \frac{18}{30} or 0.6
    q = 1 - 0.6 = 0.4
    = 0.4^2 \times 0.6^3
    = 0.03456

    The answers I have are yielding 0.0124.

    (b) more rainy days than fine days have been chosen
    P(3 rainy days) = _5C_3 \times 0.6^3 \times 0.4^2
    P(4 rainy days) = _5C_4 \times 0.6^4 \times 0.4
    P(5 rainy days) = _5C_5 \times 0.6^5
    = 0.3456 + 0.2592 + 0.007776
    = 0.612576

    The answers are yielding 0.7102

    I wonder where I am going wrong
    TIA for any assistance!
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  2. #2
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    Quote Originally Posted by lindah View Post
    Hi,

    I am having trouble with the following question:

    During winter it rains on average 18 out of 30 days. Five winter days are selected at random. Find (4 d.p) the probability that:

    (a) the first two days chosen will be fine and the remainder wet
    My approach is this is an ordered selection:

    I have defined p = it will rain = \frac{18}{30} or 0.6
    q = 1 - 0.6 = 0.4
    = 0.4^2 \times 0.6^3
    = 0.03456 .... Looks right to me

    The answers I have are yielding 0.0124.

    (b) more rainy days than fine days have been chosen
    P(3 rainy days) = _5C_3 \times 0.6^3 \times 0.4^2
    P(4 rainy days) = _5C_4 \times 0.6^4 \times 0.4
    P(5 rainy days) = _5C_5 \times 0.6^5
    = 0.3456 + 0.2592 + 0.007776 ..... 0.07776
    = 0.612576 ...... 0.68256

    The answers are yielding 0.7102

    I wonder where I am going wrong
    TIA for any assistance!
    See above
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  3. #3
    Junior Member
    Joined
    Nov 2009
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    Australia
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    Sorry for the miscalc!!!
    Then it looks like the solutions may be incorrect on this one.

    I have been tearing my brain apart on it
    Thank you!!
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