Basic Probability Concepts

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Basic Probability
8:18 — by Khan Academy

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Key Questions

  • Chances of occurrence

    Probability is simply a numerical prediction of some happening. Lets say that if I roll a die, there will be a 1/6 probability that it will end up on 1 on the die face.

  • It's a matter of converting between a fraction and a percentage .

    Remember that the word 'percent' really means 'per hundred'.
    (and you are in fact converting from dollars to cents and back)

    So if you have a probability of #0.11# you can rewrite this as
    #0.11=11/100=11%# (or #$0.11=11 cents#)

    And the other way around, if you have a chance-percentage of #45%# you can rewrite this as:
    #45%=45/100=0.45# (or #45cents=$0.45#)

    The rule:
    Fraction#->#percentage = times 100
    Percentage #-># fraction = divide by 100

    That's all there is to it.

    One more thing:
    In probabilities you never have more than #$1# or #100%#

  • Answer:

    In Probability we use the term Bernoullian trials for independent trials.

    Explanation:

    A sequence of trials are said to be Bernoullian if
    (i) there are only two outcomes for each trial ( say a success or a failure)
    (ii) Consecutive trials in the sequence are independent
    and (iii) probability of success in every trial is a constant (namely p)
    It is clear that no trial depends on the previous one here.
    Consider drawing of two cards consecutively from a well shuffled deck of cards. Consider the event that cards are both diamonds. If the draw is with replacement the trials are independent ( Bernoullian) . Otherwise they are dependent.
    In the former case the probability is ( 1/4) x (1/4)
    In the later it is( 1/4) x (12/51)

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