The margin of error, the plus or minus 3% in the above example, decreases as the sample size increases. This is only to a point. A very small sample, such as 50 respondents, has about a 14 % ...

Prob chart. For both lines, the slope is greatest near 50%. Reading off the chart, the probability of winning with a poll of sample size 1100 is around 25% if the poll result was 49%, but improves ...