P(male) = 21786/28295 = .77 and P(female)$=6509/28295 = 1 - .77=.23. Given that the numbers of men and women in the country are about equal, this means that men are quite a bit more likely to commit suicide than women -- in fact, .77/.23 is more than 3.3 times more likely.

Technical interlude: Actually the 77% and 23% figures are conditional probabilities, because they are computed on the people who committed suicide: P(male given suicide)=(21786 out of the 28295 suicides) = 77%, P(female given suicide)= 23%, similarly. What we really want, however, is not P(male given suicide) and P(female given suicide) but P(suicide given male) and P(suicide given female), because we want to compare the suicide rate among the men with that among the women. You can use the definition of conditional probability to show how these things are related, as follows:

  1. P(suicide given male) = P(suicide and male)/P(male)
  2. P(suicide given female) = P(suicide and female)/P(female)
So, P(suicide given male)/P(suicide given female)= [P(suicide and male)/P(male)]/[P(suicide and female)/P(female)].

But P(male) and P(female) are just about equal at 50% each, so P(suicide given male)/P(suicide given female)= P(suicide and male)/P(suicide and female)

Now,

  1. P(male given suicide)=P(suicide and male)/P(suicide)
  2. P(female given suicide) $=$ P(suicide and female)/P(suicide)
So, P(male given suicide)/P(female given suicide)= [P(suicide and male)/P(suicide)]/[P(suicide and female)/P(suicide)]= P(suicide and male)/P(suicide and female).

So in this special case, because the numbers of women and men are about equal, we get P(suicide given male)/P(suicide given female)= P(male given suicide)/P(female given suicide)

In other words, the ratio of suicide rates for men and women can be computed as (21786/28295)/(6509/28295)=77%/23% = 3.3, as above. Usually P(A given B) and P(B given A) lead to two quite different answers.