A possible contributor to not seeing the world as it is, is our tendency to (1) see minorities as larger than they are.
"This holds for sexual minorities, including the proportion of gays and lesbians (estimate: 30%, true: 3%), bisexuals (estimate: 29%, true: 4%), and people who are transgender (estimate: 21%, true: 0.6%)."It also applies to religious minorities, such as Muslim Americans (estimate: 27%, true: 1%) and Jewish Americans (estimate: 30%, true: 2%). And we find the same sorts of overestimates for racial and ethnic minorities, such as Native Americans (estimate: 27%, true: 1%), Asian Americans (estimate: 29%, true: 6%), and Black Americans (estimate: 41%, true: 12%)."
and (2) When we look at large groups, the proportion tends to be UNDERestimated.
"we find that people underestimate the proportion of American adults who are Christian (estimate: 58%, true: 70%) and the proportion who have at least a high school degree (estimate: 65%, true: 89%)."
Source: From millionaires to Muslims, small subgroups of the population seem much larger to many Americans | YouGov
Of course, since the work of Daniel Kahneman and Amos Tversky 50 years ago, it's been clear that people don't handle probabilities very well at all. Kahneman even won the Nobel Prize for this work (Tversky having already died).
Part of this is contamination: a bunch of extremely bad estimates are being averaged in. But if we look at the median estimates (rather than the mean) we still see a distortion. For example:
Actual % transgender: 0.6%
Mean survey estimate: 21%
Median survey estimate: 12%
Actual % with HH income over $1 million: (less than 0.5%)
Mean survey estimate: 20%
Median survey estimate: 10%
Actual % are Muslim: 1%
Mean survey estimate: 27%
Median survey estimate: 20%
Actual % are Black: 12%
Mean survey estimate: 41`%
Median survey estimate: 40%
Some of this might be a failure to consider the definition. For example, are people parsing "transgender" to include the entire spectrum of LGBTQ+? Are people confusing an INCOME of $1,000,000 a year with a NET WORTH of $1,000,000? But it's harder to make this case for a category like "Muslim" or "Black".