The table below represents the college degrees awarded in a recent academic year by gender.
Degree | Bachelor's | Master's | Doctorate | Total
-------------- | ---------- | -------- | --------- | -----
Men | 573,079 | 211,381 | 24,341 | 808,801
Women | 775,424 | 301,264 | 21,683 | 1,098,371
Total | 1,348,503 | 512,645 | 46,024 | 1,907,172
Choose a degree at random. Rounding your answer to three decimal places, find the probability that it is:
b. A doctorate or a degree awarded to a woman
e. Not a doctorate awarded to a man