Using the data below, what would be the joint probabilities, P(UÇS_j)? ? $$\begin{array} { c c c } & \begin{array} { c } \text { Prior } \ \text { Probabilities } \end{array} & \begin{array} { c } \text { Conditional } \ \text { Probabilities } \end{array} \ \text { States of Nature } ( S j ) & P ( S j ) & P ( U \mid S j ) \ \hline S 1 & 0.65 & 0.75 \ S 2 & 0.20 & 0.35 \ S 3 & 0.15 & 0.20 \ \hline \text { Total } & 1.00 & \ \hline \end{array}$$ A)0.83, 0.12, and 0.05 B)0.49, 0.07, and 0.03 C)0.47, 0.49, and 0.04 D)1.00, 0.59, and 1.00

Question

Quizplus · Accepted Answer

The joint probability P(UÇS_j) is calculated by multiplying the prior probability P(S_j) with the conditional probability P(U|S_j). For S1: 0.65 * 0.75 = 0.4875 (rounded to 0.49), for S2: 0.20 * 0.35 = 0.07, and for S3: 0.15 * 0.20 = 0.03.

Using the Data Below, What Would Be the Joint Probabilities