What fraction of a radioactive sample decays after two half.lives have elapsed?

A half-life is the time taken for half of the m of the sample to decay. So during one half-life 1/2 of the material decays. During the second half-life, half of the remaining material decays. So as 1/2 of 1/2 is 1/4, then 1/4 of the original material decays during the second half-life. If we add the material lost in the first half-life (1/2) to that lost in the second (1/4) we see that during two half-lives you would loose 3/4 of the original material, or 75%