Use the multinomial formula to find the probability for the situation in which $n = 5 , X$ $= 2 , X _ { 2 } = 2 , X _ { 3 } = 1$, and $p _ { 1 } = 0.3 , p _ { 2 } = 0.4 , p _ { 3 } = 0.3$.
A) 0.0648
B) 0.1944
C) 0.0972
D) 0.1296

Question

Quizplus · Accepted Answer

The multinomial probability is calculated using the formula: $\frac{n!}{x_1!x_2!x_3!} \cdot p_1^{x_1} \cdot p_2^{x_2} \cdot p_3^{x_3}$. Substituting the given values: $\frac{5!}{2!2!1!} \cdot 0.3^2 \cdot 0.4^2 \cdot 0.3^1 = 0.1296$.

Use the Multinomial Formula to Find the Probability for the Situation