People generally apply to lots of programs because it is a competitive process. The number you decide to apply to depends upon a number of factors (whether you are willing to move, the competitiveness of your application, etc.). The odds of getting in obviously vary depending on how competitive your application is. But, if you want to know the odds just based on probability alone, you can calculate it using the following formula where Q is the proportion of applicants rejected at a school:
Ca = (1 − (1 − Q1)(1 − Q2)(1 − Q3)...(1 − Qn)) × 100
So for example, let's say you applied to 10 schools that all accept 5% of applicants (just as an example, this will vary). The odds of acceptance (while ignoring other factors) would be 1 - (.95^10) = 40%. Thus, you can see why many people apply to lots of programs.