By the second morning of jury selection in Martin Shkreli’s fraud trial in Brooklyn, more than 130 prospective jurors had been tossed out: people with vacation or work conflicts, those who had heard about the case and even several who worked in pharmaceuticals or finance, fields in which Mr. Shkreli has worked.

Judge Kiyo A. Matsumoto turned to a young woman who works in accounting and asked if she had read or heard anything about the case. Just that morning, a court officer had confiscated a juror’s copy of The New York Post with the case on the cover.

“Oh, no, never,” the woman said.

“Oh, very good,” Judge Matsumoto responded.

The next day, after lawyers and the judge had dismissed more than 300 jurors in all, the woman made it onto the jury as an alternate.

Jury selections today have moved beyond seeking the unbiased to favoring the uninformed.

Dismissing potential jurors who might favor either the prosecution or the defense has long been a tenet of the American jury system; the right to an impartial jury is guaranteed by the Constitution.