Using the multinomial formula, find the probability of the following data.
$$\begin{array} { l }
n = 8 , x _ { 1 } = 4 , x _ { 2 } = 3 , x _ { 3 } = 1 \
p _ { 1 } = 03 , p _ { 2 } = 05 , p _ { 3 } = 02
\end{array}$$
A) 0.057
B) 0.224
C) 0.014
D) 0.022

Question

Using the multinomial formula, find the probability of the following data.
$$\begin{array} { l } 
n = 8 , x _ { 1 } = 4 , x _ { 2 } = 3 , x _ { 3 } = 1 \
p _ { 1 } = 03 , p _ { 2 } = 05 , p _ { 3 } = 02
\end{array}$$
A) 0.057
B) 0.224
C) 0.014
D) 0.022

Quizplus · Accepted Answer

The multinomial formula is given by:$$P(X_1 = x_1, X_2 = x_2, ..., X_k = x_k) = \frac{n!}{x_1!x_2!...x_k!}p_1^{x_1}p_2^{x_2}...p_k^{x_k}$$In this case, we have:$$n = 8, x_1 = 4, x_2 = 3, x_3 = 1, p_1 = 0.3, p_2 = 0.5, p_3 = 0.2$$Plugging these values into the formula, we get:$$P(X_1 = 4, X_2 = 3, X_3 = 1) = \frac{8!}{4!3!1!}0.3^40.5^30.2^1 = 0.057$$Therefore, the probability of the given data is 0.057, which is choice A.

Using the Multinomial Formula, Find the Probability of the Following n=8,x1=4,x2=3,x3=1p1=03,p2=05,p3=02\begin{array} { l } n = 8 , x _ { 1 } = 4 , x _ { 2 } = 3 , x _ { 3 } = 1 \\p _ { 1 } = 03 , p _ { 2 } = 05 , p _ { 3 } = 02\end{array}n=8,x1​=4,x2​=3,x3​=1p1​=03,p2​=05,p3​=02​

Using the Multinomial Formula, Find the Probability of the Following $\begin{array} { l } n = 8 , x _ { 1 } = 4 , x _ { 2 } = 3 , x _ { 3 } = 1 \\p _ { 1 } = 03 , p _ { 2 } = 05 , p _ { 3 } = 02\end{array}$