Use the multinomial formula and find the probability for the following data.
$$\begin{array} { l }
n = 6 , X _ { 1 } = 3 , X _ { 2 } = 2 , X _ { 3 } = 1 , \
p _ { 1 } = 0.58 , p _ { 2 } = 0.25 , p _ { 3 } = 0.17
\end{array}$$
A) 0.072
B) 0.012
C) 0.002
D) 0.124

Question

Use the multinomial formula and find the probability for the following data.
$$\begin{array} { l } 
n = 6 , X _ { 1 } = 3 , X _ { 2 } = 2 , X _ { 3 } = 1 , \
p _ { 1 } = 0.58 , p _ { 2 } = 0.25 , p _ { 3 } = 0.17
\end{array}$$
A) 0.072
B) 0.012
C) 0.002
D) 0.124

Quizplus · Accepted Answer

The multinomial probability formula is given by:$$ P(X_1 = x_1, X_2 = x_2, ..., X_k = x_k) = \frac{n!}{x_1!x_2!...x_k!}p_1^{x_1}p_2^{x_2}...p_k^{x_k} $$Given $n = 6, X_1 = 3, X_2 = 2, X_3 = 1, p_1 = 0.58, p_2 = 0.25, p_3 = 0.17$, we substitute these values into the formula:$$ P = \frac{6!}{3!2!1!}(0.58)^3(0.25)^2(0.17)^1 $$$$ P = \frac{720}{12 \times 2 \times 1}(0.195112)(0.0625)(0.17) $$$$ P = 30 \times 0.195112 \times 0.0625 \times 0.17 $$$$ P \approx 0.124 $$Therefore, the correct answer is 0.124.

Use the Multinomial Formula and Find the Probability for the Following