When Zach wan ts to con Lact his girlfriend and he knows she is not at home, he is twice as likely to send her an e-mail as he is to leave a message oo her answering machine. The probability that &he responds to hls e-mail within three hours is 80%; her chances of being similarly prompt in answering a phone message increase to 90%. Suppose she responded to the message he left this morning within two hours. What is the probability that Zach was communicating with her via e-mail?