What is the difference between independent events and dependent events?

    0

    Independent Events The probability of one event happening isn’t influenced by the outcome of another.
    In mathematical terms
    ## AB events P(AnnB)=P(A)*P(B)##
    This reads: Probability of A and B happening is equal to the probability of A happening multiplied by the probability of B happening
    An equivalent definition
    ##P(A|B) = P(A)##
    This reads: The probability of A given B happened is equal the probability of A
    Example:
    Event A: Rolling a number larger than four on a die in the first roll Event B: Rolling a 6 on a die on the second roll. These events are independent because one roll of a dice doesn’t influence the outcome of another dice roll.
    Dependent Events Is the oposite.If the outcome of one event influences the probability of the other they aren’t independent
    ##P(A|B) != P(A)##
    Example:
    Event A: Rolling a number larger than four on a die Event B: Rolling a 6 on a die on the same roll. These events are dependent because as we are in the same dice roll the occurrence of event B changes the probability of event A actually it makes it 1.
    Observation:
    Pay attention that if you are dealing with more than 2 event for them to be mutually independent every possible combination of them must be. For example if we are dealing with 3 events independence means that:
    ##P(AnnBnnC)=P(A)*P(B)*P(C)##
    ## and P(AnnB) = P(A)*P(B) P(BnnC)=P(B)*P(C) P(CnnB)=P(C)*P(B)##

                                                                                                                                      Order Now