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Math Help - Probability Distributions HELP

  1. #1
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    Probability Distributions HELP

    The choco-latie candies company makes candy-coated chocolates, 40% of which are red. The production line mixes the candies randomly and packages ten per box. What is the probability that less than four candies in a given box are red?

    I would really appreciate it if someone could help me with this. I know it has something to do with this binomial distribution.
    Last edited by Kiran; January 6th 2008 at 01:05 PM.
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  2. #2
    Member Henderson's Avatar
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    Your binomial expansion would look like this:

    (.6 + .4)^{10}.

    You only need the far left of the sequence- find the coefficients and expansions for the terms with:

    (.6)^{10}, (.6)^9(.4)^1, (.6)^8(.4)^2, and (.6)^7(.4)^3. You don't need any past that, since four or more candies would be red.
    Last edited by Henderson; January 6th 2008 at 03:46 PM. Reason: LaTexing
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  3. #3
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    Quote Originally Posted by Kiran View Post
    The choco-latie candies company makes candy-coated chocolates, 40% of which are red. The production line mixes the candies randomly and packages ten per box. What is the probability that less than four candies in a given box are red?

    I would really appreciate it if someone could help me with this. I know it has something to do with this binomial distribution.
    The three-prong approach, sport:

    1. Define the random variable:

    Let X be random variable number of red coated chocs

    2. Define the distribution followed by the random variable:

    X ~ Binomial(n = 10, p = 0.4).

    It's binomial because the three criteria are satisfied:
    * There are two possible outcomes - red ('success') or not red ('failure').
    * Each trial (look at the colour of the coating) is independent
    * The probability of 'success' (getting a red) in each trial stays the same.

    The number of trials is 10 (10 chocs per box) so n = 10.
    The probability of success in a single trial (getting a red) is 0.4 so p = 0.4.

    3. Write a probability statement of the problem:

    Pr(X < 4) = ? or \Pr(X \leq 3) = ? or Pr(X = 0) + Pr(X = 1) + Pr(X = 2) + Pr(X = 3) = ?


    There are several ways to do the calculation implied in prong #3:

    (a) Use technology eg. use TI-83 to find binomcdf(10, 0.4, 3).

    (b) Use the formula for Pr(X = r) to calculate Pr(X = 0) + Pr(X = 1) + Pr(X = 2) + Pr(X = 3).

    The calculation is left for you to do.
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