Wikipedia's page on conscription actually gives a pretty good breakdown.
In WWII, males between 18 and 64 were required to register, but the selections were limited by executive order on December 5, 1942 from from 21–45 to 18–38. Assuming the citation (George Q. Flynn, The Draft, 1940–1973) is correct, 50 million men from 18 to 45 were registered. The Selective Service statistics page gives the total inductions during WWII as 10,110,104, which would indicate that the percentage would be somewhere around 20% were drafted based on registration.
By the Vietnam war, the draft age had changed to 18-26 by the Selective Service Act. The draft pool was around 27 million (apparently lifted verbatim from a paragraph from this paper), and per the Selective Service page linked above, there were 1,857,304 inductions during Vietnam. Note that Morris gives the number as 2,215,000 - this may reflect a difference in start and end dates used but they are fairly close. This would indicate that roughly 7-9% of the draft pool was conscripted.