23. If the probability that the Giants will win the NFC championship is p and if the probability that the Raiders will win the AFC championship is q .what is the probability that only one of these teams will win its respective championship? (A) pq (B) p+q-2pq (C) vert p-qvert (D) 1-pq (E) 2pq-p-q

To find the probability that only one of these teams will win its respective championship, we need to consider two scenarios: either the Giants win and the Raiders lose, or the Giants lose and the Raiders win.<br /><br />The probability of the Giants winning the NFC championship is p, and the probability of the Raiders losing the AFC championship is 1 - q. Therefore, the probability of the Giants winning and the Raiders losing is p(1 - q).<br /><br />Similarly, the probability of the Giants losing the NFC championship is 1 - p, and the probability of the Raiders winning the AFC championship is q. Therefore, the probability of the Giants losing and the Raiders winning is (1 - p)q.<br /><br />To find the probability that only one of these teams will win its respective championship, we add the probabilities of these two scenarios: p(1 - q) + (1 - p)q.<br /><br />Simplifying this expression, we get: p - pq + q - pq = p + q - 2pq.<br /><br />Therefore, the correct answer is (B) p + q - 2pq.