>>95984097I... no. That's not how probabilities work. You're argument isn't completely wrong, but your math is.
Let's take 97% as the chance a single person will be heterosexual, and the chance that identify as something non-heterosexual as 3%.
Take two people.
The chance that both would be heterosexual is
(.97)(.97) = 94.09%
The chance that exactly one would be homosexual is
(.97)*(.03) + (.03)(.97) = 5.82%
The chance that both would be non-heterosexual would be
(.03)(.03) = 0.09%
Note that 94.09% + 5.82% + 0.09% = 100%
So for nobody in a group of four to be non-heterosexual, all four would have to be heterosexual. That chance is given by
(.97)(.97)(.97)(.97) = 88.53%
And the odds of at least one non-heterosexual person is in that group of four would be
100% – 88.53% = 11.47%
Which is rather more likely than the 0.01% you proposed.
Now, the odds that you'd have 3/4 non-heterosexual people would be
(.03)(.03)(.03)(.97) + (.03)(.03)(.97)(.03) + (.03)(.97)(.03)(.03) + (.97)(.03)(.03)(.03) =
4(.03)(.03)(.03)(.97) = 0.0105%
Which unlikely in the extreme.
Even if the odds favored non-heterosexual people more, say a 15% non-heterosexual rate, you'd still get
4(.15)(.15)(.15)(.85) = 1.15%
In other words, significantly more likely to happen, but overall extremely unlikely.
