<p>@Wheaty: you are correct, the odds for a well-qualified applicant are obviously high, while there are some applicants whose odds are basically zero. It turns out that the applicability of the model in the OP encompasses both high and low probability applicants.</p>
<p>Let’s look at the example of soozievt’s daughter. According to the data provided by soozievt, her daughter achieved 5 acceptances in 8 auditions (counting only the definite acceptances noted). This gives an observed average probability of acceptance of 62.5%. For someone who had similar skills, type, and talent who applied to a similarly-applicable set of schools, their probability will be basically the same. </p>
<p>Therefore, using the model in OP, an applicant with a probability of success in any given audition of 62.5% (0.625) would only need 3 auditions to achieve a 95 percent confidence of getting at least one acceptance. Soozievt’s daughter did more than 3 and, with that high probability of success given her talent and skills matched against the schools for which she auditioned, received 5 acceptances in 8 auditions.</p>
<p>Meanwhile, there were probably applicants in the same set of auditions as soozievt’s daughter that had a lower probability of success and received only 1-2 acceptances and perhaps none. That this occurs is substantiated by the very low acceptance rates quoted in this forum for many of the top schools (some quotes are as low as 1-2%). Trying to determine how many auditions to do based on the very low overall acceptance rates would NOT be a very good strategy because it would include many applicants that had basically ZERO chance of success in the process. Hence, a well-prepared, talented applicant choosing wisely would be well-served to base their audition strategy on a higher probability of success.</p>
<p>But what probability should you use for your personal strategy? As noted in my previous posts, if you look at the CC “acceptance” threads you will see that the average number of acceptances is around 2.37 and the average number of auditions is 8.24. Therefore, using these numbers, the average acceptance rate for people who succeed and post on CC is around 29%. To achieve a 95 percent confidence of gaining at least one acceptance with a probability of success of 29%, applicants who are able to match their talent and skills in the same manner as the average of CC posters should therefore do 9 auditions using the model in the OP. If you do 9 auditions and match your talent and skills to schools BETTER than the people who post acceptances on CC, then odds are that you will receive several acceptances. If you don’t choose as wisely, then you will perhaps not fare as well.</p>
<p>Hence, for any individual, the question is “how good do you feel your chances are for the set of schools that you have chosen?” The math on this is actually a little complicated, since you may adopt a strategy something like this:</p>
<p>3 auditions at “lottery schools” where your odds are 1 in 10 (0.1 or 10%) [this is not to say that the odds are only as low as 1 in 10 for very competitive schools, they are probably very close to zero for many applicants. This is assuming that your talent/skills/type gives you a 1 in 10 chance at these schools, whatever they are]</p>
<p>3 auditions at “decent fit and higher acceptance rate” schools where your odds are pretty good, say 1 in 2 (0.5 or 50%)</p>
<p>2 auditions at “solid fit and relatively high acceptance rate” schools where your odds are very good, say 3 in 4 (0.75 or 75%)</p>
<p>Your overall odds of success are not exactly the average of the individual odds but a simple average gives a reasonable estimate for the purposes of our analysis, in this case it turns out your average overall probability would be around 27.5% and the probability of getting at least one acceptance would be approximately 93.5 percent. So, using the approach above looks reasonable. However, you may want to add one additional school to get your odds above 95 percent and the school that you add should be one where your odds are at least 27.5 percent (around 1 in 4). Adding another “lottery school” won’t help your odds much.</p>
<p>It may be that the odds for certain applicants at certain auditions are very close to 100 percent, but that seems unlikely, given the very low number of slots available, the large number of applicants, and the desire for diversity in the entrant pool on the part of schools (they don’t want to have all short, blonde, sopranos). It seems likely that several applicants of the basically the same talent, skills, and type will audition and the school will not choose all of them, no matter how high the level of talent and skill they possess.</p>