A glance at the sky raises my probability of rain to .7. As it happens, the conditional probabilities of each state given rain remain the same, and similarly for their conditional probabilities given no rain. As Jeffrey (1983, Ch. 11) points out, my new distribution P2 is therefore fixed by the law of total probability. For example, P2(RC) = P2(RC | R)P2(R)+P2(RC | ¯.
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