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Thread: Percentages versus probabilities in Probability Distribution Tables

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    Junior Member B9766's Avatar
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    Percentages versus probabilities in Probability Distribution Tables

    Struggling here. The definition of Probability Distribution in my course text is not clear. The examples don't help much.
    In Example 1 of a Probability Distribution Table they show female births with probabilities. That is to say, x = number of girls in two births where x is a random variable. So, the number of of girls can be 0, 1, or 2. Thus the probabilities are 0.25, 0.50 and 0.25 for each of the x values. I get this. No problem.

    But then the next example asks, "When randomly selecting a jail inmate convicted of DWI the probability distribution for the number x of prior DWI sentences is as described in the following table:

    x P(x)
    0 0.512
    1 0.301
    2 0.132
    3 0.055

    But, this is a table of actual percentages where P(x) is really the percentage of values found/total selected. Isn't it? It seems to me the definition of a probability distribution in this case is contradictory. In the first case it was actual probabilities and in this case it's percentages. What am I missing here?
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    Re: Percentages versus probabilities in Probability Distribution Tables

    Quote Originally Posted by B9766 View Post
    Struggling here. The definition of Probability Distribution in my course text is not clear. The examples don't help much.
    In Example 1 of a Probability Distribution Table they show female births with probabilities. That is to say, x = number of girls in two births where x is a random variable. So, the number of of girls can be 0, 1, or 2. Thus the probabilities are 0.25, 0.50 and 0.25 for each of the x values. I get this. No problem.

    But then the next example asks, "When randomly selecting a jail inmate convicted of DWI the probability distribution for the number x of prior DWI sentences is as described in the following table:

    x P(x)
    0 0.512
    1 0.301
    2 0.132
    3 0.055

    But, this is a table of actual percentages where P(x) is really the percentage of values found/total selected. Isn't it? It seems to me the definition of a probability distribution in this case is contradictory. In the first case it was actual probabilities and in this case it's percentages. What am I missing here?
    What makes you think that the second table are percentages? So far as I can see, they are probabilities.
    The probability of no priors is 0.512.
    The probability of three priors is 0.055.
    If that is not correct, then explain why not.
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    Junior Member B9766's Avatar
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    Re: Percentages versus probabilities in Probability Distribution Tables

    Quote Originally Posted by Plato View Post
    What makes you think that the second table are percentages? So far as I can see, they are probabilities.
    The probability of no priors is 0.512.
    The probability of three priors is 0.055.
    If that is not correct, then explain why not.
    Thank you Plato. That answers a lot more than you can imagine. I obviously didn't understand the math behind probabilities from chapter 4 (This is chapter 5). The statement of the problem lead me to believe the percentages were the data sample rather than the expected results. Unfortunately this is an online course but the professor doesn't take questions. I appreciate the help. I'll go back and review the probability math.
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    Re: Percentages versus probabilities in Probability Distribution Tables

    Quote Originally Posted by B9766 View Post
    Thank you Plato. That answers a lot more than you can imagine. I obviously didn't understand the math behind probabilities from chapter 4 (This is chapter 5). The statement of the problem lead me to believe the percentages were the data sample rather than the expected results. Unfortunately this is an online course but the professor doesn't take questions. I appreciate the help. I'll go back and review the probability math.
    My view of online courses is a dim one in general.
    HERE is a video that addresses your question about % verses probability.

    HERE is a website that has a wide range of topics that you can find useful.
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    Re: Percentages versus probabilities in Probability Distribution Tables

    Quote Originally Posted by B9766 View Post
    Struggling here. The definition of Probability Distribution in my course text is not clear. The examples don't help much.
    In Example 1 of a Probability Distribution Table they show female births with probabilities. That is to say, x = number of girls in two births where x is a random variable. So, the number of of girls can be 0, 1, or 2. Thus the probabilities are 0.25, 0.50 and 0.25 for each of the x values. I get this. No problem.

    But then the next example asks, "When randomly selecting a jail inmate convicted of DWI the probability distribution for the number x of prior DWI sentences is as described in the following table:

    x P(x)
    0 0.512
    1 0.301
    2 0.132
    3 0.055

    But, this is a table of actual percentages where P(x) is really the percentage of values found/total selected. Isn't it? It seems to me the definition of a probability distribution in this case is contradictory. In the first case it was actual probabilities and in this case it's percentages. What am I missing here?
    No, those are not percentages. However, it is true that if you had a large number of such inmates, approximately 0.512*100= 51.2% of them would have no prior DWI sentences, 0.301*100= 30.1% would have one prior DWI sentences, 0.132*100= 13.2% would have two prior DWI sentences, and 0.055*100= 5.5% would have three prior DWI sentences.
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