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[quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous]Mine is applying to 14. He is in the top range of scores for all of them and maybe I spend too much time on college confidential with noble peace prize winners being rejected at all their schools, but I am hoping he gets in *somewhere*.   [b]At least 10 of them have a qualified applicant admit rate of under 5%. So if I multiply that out, it's 50% [/b]and the other 4 are a little better but still I feeling like nothing is a true safety on his list.  But hoping with 14 that he will hit something.    [/quote]

That's not how the stats work.[/quote]

Generally that is how probability works, but feel free to elaborate.[/quote]

Nope, it's not even close.  For independent events (i.e., events not correlated with each other), the likelihood of the event happening at least once = 1-p^N, where p = the probability of the event NOT happening for each event and N equals the number of events.

If you have a 50/50 chance (or 50%) chance of making a basket in basketball, do you have 100% chance of making at least one shot if you make 2 shots?  No.  Assuming each basket is an independent event (not correlated with each other), your likelihood of making at least one shot are 1 minus the chance that you will miss both shots or 1-(0.5*0.5) = 75%

In the context of these 5% acceptance rates, if you apply to 10 schools and each has an acceptance rate of 0.05, your chance of NOT being accepted by each one of them is 0.95.  Again, assuming each college's decision is independent (not correlated with the decisions of other colleges), your changes of getting in to at least one (i.e., not getting rejected by all of them) = 1-(0.95)^10 = 0.4

But, of course, these events are likely not totally independent (i.e., if you get rejected from one there is probably something that makes you more likely to get rejected from others).  Which complicates the statistics....but doesn't get you closer to 0.5 in your scenario.[/quote]

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