Initially an urn contains one red and one green ball. a ball is drawn at random from the urn, observed, and then replaced. if the ball is red, then an additional red ball is placed in the urn. if the ball is green, then a green ball is added. a second ball is drawn. find the conditional probability that the first ball was red given that the second ball drawn was red.

Voters commonly condemn politicians for being insincere, but politicians often must disguise their true feelings when they make public statements. if they expressed their honest views—about, say, their party's policies—then achieving politically necessary compromises would be much more difficult. clearly, the very insincerity that people decry shows that our government is functioning well. which of the following, if true, most seriously undermines this reasoning? (a) achieving political compromises is not all that is necessary for the proper functioning of a government. (b) some political compromises are not in the best long-term interest of the government. (c) voters often judge politicians by criteria other than the sincerity with which they express their views. (d) a political party's policies could turn out to be detrimental to the functioning of a government. (e) some of the public statements made by politicians about their party's policies could in fact be sincere.