Using the Data Below, Which of the Following Would Be

Multiple Choice

Using the data below, which of the following would be the posterior probabilities, P(S_j | U) ? ?
? $$\begin{array} { c c c } \begin{array} { c } \text { States of Nature } \\( s j ) \end{array} & \begin{array} { c } \text { Prior } \\\text { Probabilities } \\P ( s j ) \end{array} & \begin{array} { c } \text { Conditional } \\\text { Probabilities } \\P ( U \mid s j ) \end{array} \\\hline s 1 & 0.65 & 0.75 \\s 2 & 0.20 & 0.35 \\s 3 & 0.15 & 0.20 \\\hline \text { Total } & 1.00 & \\\hline\end{array}$$ ?

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