At any time before either side has exercised a peremptory challenge or challenges, but not thereafter, the court may direct the clerk to draw from the jury box, in addition to the number of jurors required by law to comprise the jury, one (1) or two (2) cards bearing numbers identifying prospective jurors. All jurors so drawn shall be empaneled and shall hear the case. Should it become necessary for any reason to excuse a juror, the trial shall continue unless the number of jurors be reduced below the number required by law. If the membership of the jury exceeds the number required by law, immediately before the jury retires to consider its verdict the clerk, in open court, shall place in a box the cards bearing numbers identifying the jurors empaneled to hear the case and, after thoroughly mixing them, withdraw from the box at random a sufficient number of cards (one or two, as the case may be) to reduce the jury to the number required by law, whereupon the jurors so selected for elimination shall be excused.