这里为何用单形名词ticket?

有人问到这样一句话:

(1)Nobody thought they would have to pay for their own ticket.

这里的ticket为什么用单形而不用复形?

有些指人的复合代词,如everybody, everyone, somebody, someone, anybody, anyone, nobody, no one等,常常代之以人称代词they(them)和物主代词their,而不用he (him)和his。因此这个句子实际上等同于:

(2)Nobody thought he would have to pay for his own ticket.