Use the Multinomial Formula to Find the Probability for the Following

question 108

Multiple Choice

Use the multinomial formula to find the probability for the following situation.
$X _ { 1 } = 2 , X _ { 2 } = 2 , X _ { 3 } = 2$ when $n = 6 , p _ { 1 } = 0.3 , p _ { 2 } = 0.5 , p _ { 3 } = 0.2$

• A) \(2 ! 2 ! 2 ! ( 0.3 ) ^ {2 } ( 0.5 ) ^ { 2 } ( 0.2 ) ^ { 2 }\)
• B) \(\frac { 6 ! } { 2 ! 2 ! 2 ! } ( 0.3 ) ^ { 2 } ( 0.5 ) ^ { 2 } ( 0.2 ) ^ { 2 }\)
• C) \(\frac { 6 ! } { 2 ! 2 ! 2 ! } ( 2 ) ^ { 0.3 } ( 2 ) ^ { 0.5 } ( 2 ) ^ { 0.2 }\)
• D) \(6 ! ( 0.3 ) ^ { 2 } ( 0.5 ) ^ { 2} ( 0.2 ) ^ { 2 }\)

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Definitions:

Gasoline

A volatile, flammable liquid derived from petroleum, primarily used as fuel in internal combustion engines.

Marginal Utility

The additional satisfaction or benefit (utility) that a person receives from consuming one more unit of a good or service.

Utils

A hypothetical unit of measurement used in economics to quantify utility or the satisfaction gained from consuming goods and services.

Indifference Curve

A contour line showing all consumption bundles that yield the same amount of total utility for an individual.