The joint probabilities are summarized in the table below and we found P(I) = 0.085. Compute the posterior probabilities, rounding the results to four decimal places.

States of Nature

Prior Probabilities

P(s_j)

Conditional Probabilities

P(I|s_j)

Joint Probabilities

P(I s_j)

Posterior Probabilities

P(s_j|I)

s₁

0.4

0.1

0.04

P(s1|I)	=	P(I s1) P(I)
	=	0.04 0.085
	=

s₂

0.5

0.05

0.025

s₃

0.1

0.2

0.02