This is from Bayesian Data Analysis - Andrew Gelman 2nd edition, example on pg.11.
If theta = 1 = mother is carrier, theta = 0 = mother is non carrier and y1, y2, y3 = 3 sons, where y1 is either 1 = affected or 0 = unaffected.
I get how the posterior becomes new prior, but I don't get why new likelihood p(y1, y2, y3 = 0 | theta = .2) = .5
Hope I made the question clear. Thanks.