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Thread: Definition of Probability

  1. #1
    Super Member harpazo's Avatar
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    Definition of Probability

    A certain math site's definition of probability:

    "How likely something is to happen."

    The site goes on to say that
    "Many events can't be predicted with total certainty. The best we can say is how likely they are to happen, using the idea of probability."

    I am having trouble with the word LIKELY in the statement above.

    Let p = probability

    Let p(A) = probability of event A happening

    The math site mathisfun.com formerly defines probability this way:

    Probability of an event happening =(Number of ways it can happen)/(Total number of outcomes).

    I just can't make sense of the FORMAL definition above. I just want to make sense of everything and anything related to the formal definition.

    Explain:

    1. Number of ways a event can happen by giving examples.

    2. Total number of outcomes. What does OUTCOMES mean here?

    I know this is a ridiculous post to you who know probability very well. However, I have not formally studied probability since high school. I am 53 about to be 54. Long time ago, right?
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  2. #2
    MHF Contributor
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    Re: Definition of Probability

    Quote Originally Posted by harpazo View Post
    A certain math site's definition of probability:

    "How likely something is to happen."

    The site goes on to say that
    "Many events can't be predicted with total certainty. The best we can say is how likely they are to happen, using the idea of probability."

    I am having trouble with the word LIKELY in the statement above.

    Let p = probability

    Let p(A) = probability of event A happening

    The math site mathisfun.com formerly defines probability this way:

    Probability of an event happening =(Number of ways it can happen)/(Total number of outcomes).

    I just can't make sense of the FORMAL definition above. I just want to make sense of everything and anything related to the formal definition.

    Explain:

    1. Number of ways a event can happen by giving examples.

    2. Total number of outcomes. What does OUTCOMES mean here?

    I know this is a ridiculous post to you who know probability very well. However, I have not formally studied probability since high school. I am 53 about to be 54. Long time ago, right?
    1) Insufficient to give examples. One must count ALL successful outcomes.
    2) "Total Number of Outcomes" is insufficient. Suppose there are infinitely many outcomes?


    p(rolling 7|given one roll of two dice) = ...

    Possible outcomes 6*6 = 36

    Possible Successful Outcomes 1+6, 2+5, 3+4, 4+3, 5+2, 5+1 ==> 6

    Sometimes, the counting is finite and easy.
    Thanks from harpazo and topsquark
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    Super Member harpazo's Avatar
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    Re: Definition of Probability

    Quote Originally Posted by TKHunny View Post
    1) Insufficient to give examples. One must count ALL successful outcomes.
    2) "Total Number of Outcomes" is insufficient. Suppose there are infinitely many outcomes?


    p(rolling 7|given one roll of two dice) = ...

    Possible outcomes 6*6 = 36

    Possible Successful Outcomes 1+6, 2+5, 3+4, 4+3, 5+2, 5+1 ==> 6

    Sometimes, the counting is finite and easy.
    I am referring to basic probability not advanced topics.

    Samples:

    Let A = rapture event happening today

    P(A) = uncertain for the specific date of the event is not given.

    Let B = I will turn into a butterfly

    P(B) = 0 because there is no chance WHATSOEVER that I will become a butterfly in this life or the next.

    Do you agree with my examples?
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    Re: Definition of Probability

    Quote Originally Posted by harpazo View Post
    I am referring to basic probability not advanced topics.
    Samples:
    Let A = rapture event happening today
    P(A) = uncertain for the specific date of the event is not given.
    Look the $\Large{\mathscr{P}(\text{rapture})=0}$
    The idea of rapture is a Biblical fiction. SEE HERE.
    If you are interest in real scholarship, then write Bart, there are hardship grants for that blog that I have sponsored.
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  5. #5
    Super Member harpazo's Avatar
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    Re: Definition of Probability

    Quote Originally Posted by Plato View Post
    Look the $\Large{\mathscr{P}(\text{rapture})=0}$
    The idea of rapture is a Biblical fiction. SEE HERE.
    If you are interest in real scholarship, then write Bart, there are hardship grants for that blog that I have sponsored.
    Thanks. Can we get back to my question concerning a simple, "math for dummies" definition of basic probability? I will check out the link provided.
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