Question
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
Solution
3.4
(136 Votos)
Antônio
Mestre · Tutor por 5 anos
Resposta
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.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).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.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.Simplifying this expression, we get: p - pq + q - pq = p + q - 2pq.Therefore, the correct answer is (B) p + q - 2pq.