Pr(AB) = Probability that bag with 99 reds is drawn and 1 red is drawn from that bag = 1/2 * 99/100 = 99/200.

Pr(B) = Probability that a red is drawn = ((1/2)*(99/100) + (1/2)*(1/100)) = 100/200 = 1/2.

Pr(AB)/Pr(B) = (99/200)/(100/200) = 99/100.

Michael Shackleford, A.S.A.