Currently a college senior, Jeremy has had a secret crush on Emma ever since the third grade. Two weeks ago, fearing that his feelings would forever go unrequited, he broke his silence and sent Emma a letter through Campus Mail, acknowledging his twelve-year secret romance. Now, fourteen agonizing days later, he has yet to receive a response. Hoping against hope, Jeremy and his fragile psyche are clinging to the possibility that someone's letter was lost in the mail. Assume that (1) Emma (who is actually secretly dating Jeremy's father) has a 70% chance of mailing a response if, in fact, she had received the letter and (2) the Campus Post Office has a one in fifty chance of losing any particular piece of mail. Since Jeremy has not received a response, what is the probability that Emma never received Jeremy's confession of the heart?
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