Why Mildred tries to suicide in the first chapter ?
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Mildred actually doesn't try to kill herself. She simply takes so many pills that she can't remember what she's taken. She doesn't even remember it the next morning.
I'm not sure why you erased your second question, but in answer, Mildred couldn't understand why Montag was so obsessed by the books, nor why he'd put them in danger by keeping them in their home (or buried nearby). She called in the alarm in order to save herself, knowing that suspicion already surrounded Montag.