Bayes by hand

Use the prior $(0.5,0.3,0.2)$ over (deal, stalemate, escalation) from 12.5. (a) Reproduce the posterior after news 1 (likelihoods $0.2,0.6,0.9$) and then news 2 (likelihoods $0.8,0.5,0.1$). Show every step. (b) What likelihood ratio, escalation against "not escalation", is needed to move $P(\text{escalation})$ from 0.2 to 0.5? (c) Verify that applying the two news items in reverse order gives the same posterior.