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Tuesday, 1 July 2014

Multiplication Rule

  Manoj       Tuesday, 1 July 2014


Definition:
The definition of conditional probability in equation can be rewritten to provide a general expression for the probability of the intersection of two events. This formula is referred to as a multiplication rule for probabilities.
P(AB) = P(BA)P(A) = P(AB)P(B)
The last expression in above Equation is obtained by interchanging $A$ and $B$.
Example:
The probability that an automobile battery subject to high engine compartment temperature suffers low charging current is $0.7$. The probability that a battery is subject to high engine compartment temperature is $0.05$.
Let $C$ denote the event that a battery suffers low charging current, and let $T$ denote the event that a battery is subject to high engine compartment temperature. The probability that a battery is subject to low charging current and high engine compartment temperature is
P(CT) = P(CT)P(T) = 0.7 × 0.05 = 0.035
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