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    Probability of Events n(A) = 13, n(B) = 4 from n = 52

    Probability Calculator

    Find the probability of n(A), n(A'), n(B), n(B'), n(AUB) & n(A∩B) for n(A) = 13, n(B) = 4 from the sample space of total events n = 52. The below is the calculation summary for probability of each function such as P(A), P(A'), P(B), P(B'), P(AUB) & P(A∩B) for events n(A) = 13 & n(B) = 4 from total events of experiment n = 52.

    Calculation Summary
    Total Events n52
    Total Events n(A)13
    Total Events n(B)4
    P(A)0.25
    P(A')0.75
    P(B)0.08
    P(B')0.92
    P(A∩B)0.02
    P(AUB)0.31
    P(A|B)0.25

    Work with Steps for P(A) & P(B) from n(A) = 13, n(B) = 4 & n = 52

    The below is the work with steps shows how to find the probability of P(A), P(A'), P(B), P(B'), P(AUB) & P(A∩B) for n(A) = 13, n(B) = 4 from the total events n = 52 may help grade school students to solve the probability worksheet problems efficiently.
    Probability formulas used in this calculation
    P(A) = Number of Successful Events / Total Events of Sample Space

    P(A) = n(A)/n

    P(B) = n(B)/n

    P(A∩B) = P(A) x P(B)

    P(AUB) = P(A) + P(B) - P(A∩B)
    P(A|B) = P(A∩B)/P(B)

    P(A') = 1 - P(A)

    P(B') = 1 - P(B)

    Steps to find P(A) and P(A')
    P(A) = 13/52
    = 0.25
    P(A) = 0.25
    P(A') = 1 - P(A)
    P(A') = 1 - 0.25
    P(A') = 0.75
    0.25 is the probability of events n(B) and 0.75 is the probability of not occuring events n(B).

    Steps to find P(B) and P(B')
    P(B) = 4/52
    = 0.08
    P(B) = 0.08
    P(B') = 1 - P(B)
    P(B') = 1 - 0.08
    P(B') = 0.92
    0.08 is the probability of events n(B) and 0.92 is the probability of not occuring events n(B).

    Steps to find P(A∩B)
    P(A∩B) = 0.25 x 0.08
    = 0.02
    P(A∩B) = 0.02
    0.31 is the probability of both events n(A) and n(B) occur.

    Steps to find P(AUB)
    P(AUB) = 0.25 + 0.08 - 0.02
    = 0.31
    P(AUB) = 0.31
    0.31 is the probability of events n(A) or n(B) or both n(A) and n(B) occur.

    Steps to find conditional probability P(A|B)
    P(A|B) = P(A∩B)/P(B)=0.02/0.08
    = 0.25
    P(A|B) = 0.25

    0.75 is the conditional probability of event n(A) = 13, n(B) = 4 and total events n = 52.

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