Research  Chapman (1967) described a bias in the judgment of the frequency with which
two events co-occur. This demonstration showed that the  co-occurrence
 of paired stimuli resulted in
participants overestimating the frequency of the pairings.  [7]  To test this
idea, participants were given information about several hypothetical mental
patients. The data for each patient consisted of a clinical diagnosis and a
drawing made by the patient. Later, participants estimated the frequency with
which each diagnosis had been accompanied by various features of the drawing.
The subjects vastly overestimated the frequency of this co-occurrence (such as
suspiciousness and peculiar eyes). This effect was labeled the  illusory
correlation  . Tversky and
Kahneman suggested that availability provides a natural account for the
illusory-correlation effect. The strength of the association between two
events could provide the basis for the judgment of how frequently the two
events co-occur. When the association is strong, it becomes more likely to
conclude that the events have been paired frequently. Strong associations will
be thought of as having occurred together frequently.  [8]

In Tversky & Kahneman's first examination of availability heuristics, subjects
were asked, "If a random word is taken from an English text, is it more likely
that the word starts with a K, or that K is the third letter?" They argue that
English-speaking people would immediately think of many words that begin with
the letter "K" (kangaroo, kitchen, kale), but that it would take a more
concentrated effort to think of any words in which "K" is the third letter
(acknowledge, ask). Results indicated that participants overestimated the
number of words that began with the letter "K" and underestimated the number
of words that had "K" as the third letter. Tversky and Kahneman concluded that
people answer questions like these by comparing the availability of the two
categories and assessing how easily they can recall these instances. In other
words, it is easier to think of words that begin with "K", more than words
with "K" as the third letter. Thus, people judge words beginning with a "K" to
be a more common occurrence. In reality, however, a typical text contains
twice as many words that have "K" as the third letter than "K" as the first
letter.  [8]

In Tversky and Kahneman's seminal paper, they include findings from several
other studies, which also show support for the availability heuristic. Apart
from their findings in the "K" study, they also found:

When participants were shown two visual structures and asked to pick the structure that had more paths, participants saw more paths in the structure that had more obvious available paths. In the structure that participants chose, there were more columns and shorter obvious paths, making it more available to them. When participants were asked to complete tasks involving estimation, they would often underestimate the end result. Participants were basing their final estimation on a quick first impression of the problem. Participants particularly struggled when the problems consisted of multiple steps. This occurred because participants were basing their estimation on an initial impression. Participants failed to account for the high rate of growth in the later steps due to the impression they formed in the initial steps. This was shown again in a task that asked participants to estimate the answer to a multiplication task, in which the numbers were presented as either 1x2x3x4x5x6x7x8 or 8x7x6x5x4x3x2x1. Participants who were presented the equation with the larger numbers first (8x7x6...), estimated a significantly higher result than participants with the lower numbers first (1x2x3...). Participants were given a short amount of time to make the estimation, thus participants based their estimates off of what was easily available, which in this case was the first few numbers in the sequence.  [8]