Probability of missing 100 free throws

[boyznum1]

1. 0.5^100 = 7.8886091e-31[/size]

 

2. Yes[/size]

 

3. Yes[/size]

Can you put #1 into simpler terms such as days or a fraction maybe?

[dimreepr]

Can you put #1 into simpler terms such as days or a fraction maybe?

 

 

The point is, it doesn't matter...

[tar]

7.3 septillion years of 100 shots every 5 minutes and ONE time on average during the 7.3 septillion years you should miss 100 in a row...and the numbers don't matter?

 

Half a quadrillion times the age of the universe 'til the event is probably going to occur, and the numbers don't matter, because it could happen tomorrow?

 

I don't know, at what point a probability is so low as that it should be considered zero...for all intents and purposes...as in, it is not likely to happen in your lifetime. Or put another way, it is not going to happen in your lifetime.

[boyznum1]

7.3 septillion years of 100 shots every 5 minutes and ONE time on average during the 7.3 septillion years you should miss 100 in a row...and the numbers don't matter?Half a quadrillion times the age of the universe 'til the event is probably going to occur, and the numbers don't matter, because it could happen tomorrow?I don't know, at what point a probability is so low as that it should be considered zero...for all intents and purposes...as in, it is not likely to happen in your lifetime. Or put another way, it is not going to happen in your lifetime.

It actually does matter if you consider everybody who's ever played basketball. It actually becomes quite interesting when you explore the fact in all likelihood it has or will happen. Not my original question, but still an interesting outlook.

[tar]

but here is where the numbers do matter

 

Before, with the 1 in 3 shooter we knocked the odds down to 1 in 2000 which seems possible. But with the 50 50 shooter the odds are way more remote that they will miss 100 in a row. Even dividing the years it would take one 50 50 shooter to probably miss all 100 of a 100 trial set by 500,000,000, or the number of basketball players currently around, you still get a length of time required, that is 1 million times the age of the universe.

 

So it matters greatly, in your debate with your head coach, what the caliber of player you are coaching. If you are coaching NBA players that shoot better than 50 percent then you are not going to see a trial of 100 where the guy misses all of them...unless he is injured or drunk, or otherwise compromised. On the other hand, if you are coaching a group that shoots a lot worse than 1 in three, like one in four or 1 in 5 or whatever, then you are entering a situation where a miss of 100 in a row is within the realm of possibility. That is, that the numbers would allow someone that does not shoot very well to miss 100 in a row, at some point since the beginning of basketball foul shooting. Or in terms of the OP question, it matters what kind of foul shooter you are considering, before you can calculate the odds of missing 100 in a row.

 

Regards, TAR

Edited October 11, 2016 by tar

[tar]

Dr. Krettin

 

What are the odds if you don't constrain yourself to 100 trial sets, but shoot continuously so that any streak of 100 misses count. As in you miss the last 75 of your first set and miss the first 25 of your second set?

 

Regards, TAR

[DrKrettin]

Dr. Krettin

 

What are the odds if you don't constrain yourself to 100 trial sets, but shoot continuously so that any streak of 100 misses count. As in you miss the last 75 of your first set and miss the first 25 of your second set?

 

Regards, TAR

 

 

Let's say each shot is 50%. You keep shooting until you get a miss. That miss is the first of a possible series of 100 misses, so the probability after that first missed shot is 0.5^99 = 1.5777218e-30

[Prometheus]

The expectation of the number of attempts before achieving n consecutive successes (or misses in this case), is given by:

 

[math]\frac{1-p^{-n}}{p-1}[/math]

 

Derived here.

 

Assuming an average hit rate of 70% then you'd expect 2.7 x 10^52 attempts to get 100 consecutive misses.

 

Some-one more clever than me could then probably then use a zero-one law to prove the chance of this occurring in infinitely many attempts is 1.

[swansont]

!

Moderator Note

 

General discussion on probability is now in its own thread.

http://www.scienceforums.net/topic/99570-probability-split-from-free-throws/

 

[Country Boy]

First, what is this "law of infinite probability"? I have never heard of such a thing. Second, if a basketball player has a probability "p" or making a free throw then he has a probability of 1- p of missing a free throw. Assuming that every shot is independent of every other shot, the probabliity of missing 100 free throws in a row is [math](1- p)^{100}[math]. If p is close to 1, that will be very close to 0 but not 0. I don't know what "functionally 0" means but, mathematically, there is always a probability that a good free thrower will miss 100 shots in a row.