A polling firm, hired to estimate the likelihood of the passage of an up-coming referendum, obtained the set of survey responses to make its estimate. The encoding system for the data is:   If the referendum were held today, estimate the probability that it would pass.

 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0

To estimate the likelihood of the passage of the upcoming referendum based on the given survey responses, you can calculate the proportion of "1" responses (indicating a vote in favor of the referendum) out of the total number of responses.

In this case, the set of survey responses is:
0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0

Counting the number of "1" responses, we find that there are 8 "1"s in the set.

To calculate the likelihood of passage, divide the number of "1" responses by the total number of responses:

Likelihood of passage = 8 / 20

This simplifies to:

Likelihood of passage = 0.4 = 40%

Therefore, based on the survey responses, the estimated probability of the referendum passing would be 40%.