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Math Help - probability help!

  1. #1
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    Question probability help!

    can show me how to do this step by step plz!!


    The table below shows the results of rolling a fair number cube 50 times during a classroom activity.

    # cube data

    outcome|Frequency
    1 | 7
    2 |12
    3 |10
    4 |9
    5 |8
    6 | 4


    What is the difference between the theoretical probability of rolling a number less than 4 and the experimental results recorded in the table above?
    F.8%
    G.79%
    H.58%
    J.29%
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  2. #2
    Member
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    Quote Originally Posted by whatxxever_2009 View Post
    can show me how to do this step by step plz!!


    The table below shows the results of rolling a fair number cube 50 times during a classroom activity.

    # cube data

    outcome|Frequency
    1 | 7
    2 |12
    3 |10
    4 |9
    5 |8
    6 | 4


    What is the difference between the theoretical probability of rolling a number less than 4 and the experimental results recorded in the table above?
    F.8%
    G.79%
    H.58%
    J.29%
    What is the theoretical probability of rolling a number less than four?
    When the problem says theoretical probability of a fair cube, you assume that every outcome is equally likely.

    The theoretical probability of rolling a number less than 4 with a fair, 6 sided dice is 50% or 3/6=1/2. This is because you can roll either a 1, 2, 3, 4, 5 or 6. half of those outcomes qualify as "less than four".

    To get the experimental result you have to do some more arithmetic.
    7+12+10=29. There are 29, out of 50 trials, where the dice landed on less than 4. so the experimental results are that 29/50=58% of dice rolls are less than 4.

    So the difference between the theoretical probability and the observed, experimental results is 58-50=8%
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  3. #3
    Senior Member Twig's Avatar
    Joined
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    Gothenburg
    Posts
    396

    hi

    Hi

    robeuler already gave you an answer, this should be posted in the probability section though.

    In general, the classical approach for estimating probabilities is through the frequentist approach used here:

    Let A = "Dice showing less than 4", then

     P(A) \approx \frac{\mbox{Number of times showing less than 4}}{\mbox{Total number of trials}}

    Note the  \approx sign, because we would need an infinite number of trials to be certain about the true probability.

    Thus,  \lim_{n\rightarrow \infty} \frac{N_{A}}{N} = P(A)
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