if the probability that the Giants will win the NFC championship is p and if the probability that the raiders will wini the AFC championship is q, what is the probability that only one of these teams will win its respectgive championship?

Options

A. pq
B. `p+q-2pq`
C. `|p-q|`
D. `1-pq`

Answer

B

Explanation

The probability that both teams will win is pq. The probability that both will lose is (1-p)(1-q). The probability that only one will winn is `1-[pq+(1-q)(1-q)]=1-(pq+1-p-q+pq)=p+q-2pq`.
Alternative solution: the probability that the giants will win and the raiders will lose is p(1-q). the probability that the raiders will win and the giants will lose is q(1-p). therefore, the probability that either one of these results will occurs is `p(1-q)+q(1-p)=p+q-2pq`.