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) \(6 ! ( 0.3 ) ^ { 2 } ( 0.5 ) ^ { 2} ( 0.2 ) ^ { 2 }\)

---

Definitions:

Q

Quantity, frequently used in economic equations and discussions to denote the amount of goods produced or consumed.

PQ

The product of price (P) and quantity (Q), often used in economics to calculate total revenue or expenditure.

P

Typically refers to "Price" in economic models, representing the monetary value assigned to a good or service in the market.

V

Typically stands for Velocity in economic contexts, referring to the rate at which money circulates in the economy.