multiplication rule

(noun)

The probability that A and B occur is equal to the probability that A occurs times the probability that B occurs, given that we know A has already occurred.

Related Terms

Examples of multiplication rule in the following topics:

  • The Multiplication Rule

  • The Multiplication Rule

    • The multiplication rule states that the probability that $A$ and $B$ both occur is equal to the probability that $B$ occurs times the conditional probability that $A$ occurs given that $B$ occurs.
    • This rule can be written:
    • We obtain the general multiplication rule by multiplying both sides of the definition of conditional probability by the denominator.
    • That is, in the equation $\displaystyle P(A|B)=\frac{P(A\cap B)}{P(B)}$, if we multiply both sides by $P(B)$, we obtain the Multiplication Rule.
    • Apply the multiplication rule to calculate the probability of both $A$ and $B$ occurring

  • General multiplication rule

    • Section 2.1.6 introduced the Multiplication Rule for independent processes.
    • Here we provide the General Multiplication Rule for events that might not be independent.
    • This General Multiplication Rule is simply a rearrangement of the definition for conditional probability in Equation (2.40) on page 83.
    • We will compute our answer using the General Multiplication Rule and then verify it using Table 2.16.
    • Among the 96.08% of people who were not inoculated, 85.88% survived:P(result = lived and inoculated = no) = 0.8588 × 0.9608 = 0.8251 This is equivalent to the General Multiplication Rule.

  • Student Learning Outcomes

  • Summary of Formulas

  • Addition, Subtraction, and Multiplication

    • Complex numbers are added by adding the real and imaginary parts; multiplication follows the rule $i^2=-1$.
    • The multiplication of two complex numbers is defined by the following formula:
    • The preceding definition of multiplication of general complex numbers follows naturally from this fundamental property of the imaginary unit.
    • Indeed, if i is treated as a number so that di means d time i, the above multiplication rule is identical to the usual rule for multiplying the sum of two terms.
    • = $ac + bdi^2 + (bc + ad)i$ (by the commutative law of multiplication)

  • The Chain Rule

    • For example, following the chain rule for $f \circ g(x) = f[g(x)]$ yields:
    • The chain rule can also be generalized to multiple variables in cases where the nested functions depend on more than one variable.
    • Using the chain rule yields:
    • Use of the chain rule is needed for the complicated calculation.
    • Calculate the derivative of a composition of functions using the chain rule

  • The Chain Rule

    • The chain rule is a formula for computing the derivative of the composition of two or more functions.
    • For example, the chain rule for $f \circ g$ is $\frac {df}{dx} = \frac {df}{dg} \, \frac {dg}{dx}$.
    • The chain rule above is for single variable functions $f(x)$ and $g(x)$.
    • However, the chain rule can be generalized to functions with multiple variables.
    • The chain rule can be used to take derivatives of multivariable functions with respect to a parameter.

  • The Law of Multiple Proportions

    • The law of multiple proportions states that elements combine in small whole number ratios to form compounds.
    • The law of multiple proportions, also known as Dalton's law, was proposed by the English chemist and meteorologist John Dalton in his 1804 work, A New System of Chemical Philosophy.
    • It is a rule of stoichiometry.
    • Dalton's law of multiple proportions is part of the basis for modern atomic theory, along with Joseph Proust's law of definite composition (which states that compounds are formed by defined mass ratios of reacting elements) and the law of conservation of mass that was proposed by Antoine Lavoisier.

  • Winning an Election: Majority, Plurality, and Proportional Representation

    • Majority rule is a decision rule that selects the option which has a majority, that is, more than half the votes.
    • Some scholars have recommended against the use of majority rule, at least under certain circumstances, due to an ostensible trade-off between the benefits of majority rule and other values important to a democratic society.
    • Being a binary decision rule, majority rule has little use in public elections, with many referendums being an exception.
    • In political science, the use of the plurality voting system alongside multiple, single-winner constituencies to elect a multi-member body is often referred to as single-member district plurality (SMDP).
    • Compare and contrast the voting systems of majority rule, proportional representation and plurality voting