According to Rashi, the serpent desired Eve and his plan was that Adam eat from the tree and die so that he can have her [Rashi Genesis 3:1, Bereishis Rabbah 18:6]. If that was his plan, why would he cause her to eat from the tree first? Obviously, if he thought Adam would die from eating, Eve would too.
The מהר"ל (גור אריה ג-טו) asks your question and he suggests that the snake thought that Chava, as a good wife, would offer the fruit to her husband first. The serpent expected him to die straight away, after which she would refrain from eating! כי עשית זאת - ...ואם תאמר אחר שנתכוון לישא את חוה, הרי אם תאכל תמות? ויש לומר שחשב שדרך נשים לכבד בעליהן, ותתן לו קודם ולא תמות, כי תראה מיתת בעלה מיד ולא תאכל עוד.