The bear alarm at grizzly's peak ski resort sounds an average of once every thirty days, but the alarm is so sensitively calibrated that it sounds an average of ten false alarms for every undetected bear. despite this, the alarm only sounds for three out of four bears that actually appear at the resort. if the alarm sounds, what is the probability that a bear has actually been sighted?

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.